<PAGE>   1
                                                                     EXHIBIT 2.4





                             CERTIFICATE OF MERGER

                                       OF

                        MERCURY ACQUISITION CORPORATION

                                 WITH AND INTO

                        THERMADYNE HOLDINGS CORPORATION

                          (Pursuant to Section 251 of
             the General Corporation Law of the State of Delaware)

                                   * * * * *

         The undersigned does hereby certify that:

         FIRST:  The name and state of incorporation of each of the constituent
corporations is as follows:


NAME                                               STATE OF INCORPORATION

Thermadyne Holdings Corporation                    Delaware

Mercury Acquisition Corporation                    Delaware


         SECOND:  An Agreement and Plan of Merger dated as of January 20, 1998,
and as amended on April 23, 1998, between Thermadyne Holdings Corporation and
Mercury Acquisition Corporation (the "AGREEMENT") has been approved, adopted,
certified, executed and acknowledged by each of the constituent corporations in
accordance with the requirements of Section 251(c) of the General Corporation
Law of the State of Delaware.

         THIRD:  The name of the surviving corporation is Thermadyne Holdings
Corporation.
<PAGE>   2
         FOURTH: Upon the effectiveness of the merger, the Restated Certificate
of Incorporation of the Surviving Corporation shall read in its entirety as
follows:

                 FIRST:  The name of the Corporation is Thermadyne Holdings
         Corporation.

                 SECOND: The address of its registered office in the State of
         Delaware is 1013 Centre Road, Wilmington, Delaware 19805.  The name of
         its registered agent at such address is Corporation Service Company.

                 THIRD:  The purpose of the Corporation and the nature and
         objects of the business to be transacted, promoted, and carried on are
         to engage in any lawful act or activity for which corporations may be
         organized under the General Corporation Law of the State of Delaware,
         as the same exists or may hereafter be amended (the "Delaware Law").

                 FOURTH: The total number of shares of stock which the
         Corporation shall have authority to issue is 45,000,000, consisting of
         30,000,000 shares of Common Stock, par value $0.01 per share (the
         "COMMON STOCK"), and 15,000,000 shares of Preferred Stock, par value
         $0.01 per share (the "PREFERRED STOCK"), of which 2,000,000 shares
         have been designated 13% Senior Exchangeable Preferred Stock (the
         "SENIOR PREFERRED STOCK").

                 The designations and the powers and preferences, rights,
         qualifications, limitations and restrictions of the Common Stock and
         the Preferred Stock are as follows:

                 A.       Provisions Relating to the Common Stock

                 Except as otherwise required by law, each holder of Common
         Stock shall be entitled to one vote for each share of Common Stock
         standing in such holder's name on the records of the Corporation on
         each matter submitted to a vote of the stockholders.

                 The holders of the Common Stock shall be entitled to receive
         when, as, and if declared by the board of directors of the
         Corporation, out of funds legally available therefor, dividends
         payable in cash, stock, or otherwise.





                                       2
<PAGE>   3
                 Upon any liquidation, dissolution, or winding up of the
         Corporation, whether voluntary or involuntary, and after the holders
         of any bonds, debentures, or other obligations of the Corporation
         shall have been paid in full the amounts to which they shall be
         entitled (if any), or a sum sufficient for such payment in full shall
         have been set aside, the remaining net assets of the Corporation shall
         be distributed pro rata to the holders of the Common Stock in
         accordance with their respective rights and interests, to the
         exclusion of the holders of any bonds, debentures, or other
         obligations of the Corporation.

                 The Corporation may issue shares of its Common Stock from time
         to time for such consideration (in any form, but not less in value
         than the par value thereof) as may be fixed by the board of directors
         of the Corporation, which is expressly authorized to fix the same in
         its absolute and uncontrolled discretion subject to the foregoing
         conditions. Shares so issued for which the consideration shall have
         been paid or delivered to the Corporation shall be deemed fully paid
         stock and shall not be liable to any further call or assessment
         thereon, and the holders of such shares shall not be liable for any
         further payments in respect of such shares.  The Corporation shall
         also have authority to create and issue rights and options entitling
         their holders to purchase or otherwise acquire shares of Common Stock
         and such rights and options shall be evidenced by instrument(s)
         approved by the board of directors of the Corporation. The board of
         directors of the Corporation shall be empowered to set the exercise
         price, duration, times for exercise, and other terms of such options
         or rights; provided, however, that the consideration to be received
         (which may be in any form) for any shares of Common Stock subject
         thereto shall have a value not less than the par value thereof.

                 B.       Provisions Relating to the Preferred Stock

                 The Board of Directors is hereby empowered to authorize by
         resolution or resolutions from time to time the issuance of one or
         more classes or series of Preferred Stock and to fix the designations,
         powers, preferences and relative, participating, optional or other
         rights, if any, and the qualifications, limitations or restrictions
         thereof, if any, with respect to each such class or series of
         Preferred Stock and the number of shares constituting each such class
         or series, and to increase or decrease the number of shares of





                                       3
<PAGE>   4
         any such class or series to the extent permitted by the Delaware Law.

                 C.       Provisions Relating to the Senior Preferred Stock

                 (1) NUMBER AND DESIGNATION.  2,000,000 shares of the Preferred
         Stock of the Corporation shall be designated as 13% Senior
         Exchangeable Preferred Stock.

                 (2) RANK. The Senior Preferred Stock shall, with respect to
         dividend rights and rights on liquidation, dissolution and winding up,
         rank prior to all classes of or series of common stock of the
         Corporation, including the Common Stock, and each other class of
         capital stock of the Corporation, the terms of which provide that such
         class shall rank junior to the Senior Preferred Stock or the terms of
         which do not specify any rank relative to the Senior Preferred Stock.
         All equity securities of the Corporation to which the Senior Preferred
         Stock ranks prior (whether with respect to dividends or upon
         liquidation, dissolution, winding up or otherwise), including the
         Common Stock, are collectively referred to herein as the "JUNIOR
         SECURITIES." All equity securities of the Corporation with which the
         Senior Preferred Stock ranks on a parity (whether with respect to
         dividends or upon liquidation, dissolution or winding up) are
         collectively referred to herein as the "PARITY SECURITIES." The
         respective definitions of Junior Securities and Parity Securities
         shall also include any rights or options exercisable for or
         convertible into any of the Junior Securities and Parity Securities,
         as the case may be. The Senior Preferred Stock shall be subject to the
         creation of Junior Securities.

                 (3) DIVIDENDS. (a)  (i) The holders of shares of Senior
         Preferred Stock shall be entitled to receive, when, as and if declared
         by the Board of Directors, out of funds legally available for the
         payment of dividends, dividends (subject to Sections 3(a)(ii) and
         (iii) hereof) at a rate equal to 13% per annum (computed on the basis
         of a 360 day year) (the "DIVIDEND RATE") on the Liquidation Value of
         each share of Senior Preferred Stock on and as of the most recent
         Dividend Payment Date (as defined below). In the event the Corporation
         is unable or shall fail to discharge its obligation to redeem all
         outstanding shares of Senior Preferred Stock pursuant to paragraph
         5(c) or 5(d) hereof, the Dividend Rate shall increase by .25 percent
         per quarter (each, a "DEFAULT DIVIDEND") for each quarter or portion
         thereof following the date





                                       4
<PAGE>   5
         on which such redemption was required to be made until cured, provided
         that the aggregate increase shall not exceed 5%. Such dividends shall
         be payable in the manner set forth below in Sections 3(a)(ii) and
         (iii) quarterly on March 31, June 30, September 30, and December 31 of
         each year (unless such day is not a business day, in which event on
         the next succeeding business day) (each of such dates being a
         "DIVIDEND PAYMENT DATE" and each such quarterly period being a
         "DIVIDEND PERIOD"). Such dividends shall be cumulative from the date
         of issue, whether or not in any Dividend Period or Periods there shall
         be funds of the Corporation legally available for the payment of such
         dividends.

                 (ii) Prior to the fifth anniversary of the issuance of the
                 Senior Preferred Stock (the "CASH PAY DATE"), dividends shall
                 not be payable in cash to holders of shares of Senior
                 Preferred Stock but shall, subject to Section 3(b) hereof,
                 accrete to the Liquidation Value in accordance with Section
                 4(a) hereof.

                 (iii) Following the Cash Pay Date, each such dividend shall be
                 payable in cash on the Liquidation Value per share of the
                 Senior Preferred Stock, in equal quarterly amounts (to which
                 the Default Dividend, if any, shall be added), to the holders
                 of record of shares of the Senior Preferred Stock, as they
                 appear on the stock records of the Corporation at the close of
                 business on such record dates, not more than 60 days or less
                 than 10 days preceding the payment dates thereof, as shall be
                 fixed by the Board of Directors. Accrued and unpaid dividends
                 for any past Dividend Periods may be declared and paid at any
                 time, without reference to any Dividend Payment Date, to
                 holders of record on such date, not more than 45 days
                 preceding the payment date thereof, as may be fixed by the
                 Board of Directors.

                 (b) At the written request of the holders of a majority of the
         shares of Senior Preferred Stock, the Corporation shall, commencing on
         the first Dividend Payment Date after such request and ending on the
         Cash Pay Date, be required to pay all dividends on shares of Senior
         Preferred Stock by the issuance of additional shares of Senior
         Preferred Stock ("ADDITIONAL SHARES"). The Additional Shares shall be
         identical to all other shares of Senior





                                       5
<PAGE>   6
         Preferred Stock, except as set forth in Section 4. For the purposes of
         determining the number of Additional Shares to be issued as dividends
         pursuant to this Paragraph (b), such Additional Shares shall be valued
         at their Applicable Liquidation Value as provided in Section 4(c).

                 (c)  Holders of shares of Senior Preferred Stock shall not be
         entitled to any dividends, whether payable in cash, property or stock,
         in excess of the cumulative dividends, as herein provided, on the
         Senior Preferred Stock. Except as provided in this Section 3, no
         interest, or sum of money in lieu of interest, shall be payable in
         respect of any dividend payment or payments on the Senior Preferred
         Stock that may be in arrears.

                 (d)  So long as any shares of the Senior Preferred Stock are
         outstanding, no dividends, except as described in the next succeeding
         sentence, shall be declared or paid or set apart for payment on Parity
         Securities, for any period unless (to the extent such dividends are
         payable in cash) full cumulative dividends have been or
         contemporaneously are declared and paid or declared and a sum
         sufficient for the payment thereof set apart for such payment on the
         Senior Preferred Stock for all Dividend Periods terminating on or
         prior to the date of payment of the dividend on such class or series
         of Parity Securities. When (to the extent such dividends are payable
         in cash) dividends are not paid in full or a sum sufficient for such
         payment is not set apart, as aforesaid, all dividends declared upon
         shares of the Senior Preferred Stock and all dividends declared upon
         any other class or series of Parity Securities shall (in each case, to
         the extent payable in cash) be declared ratably in proportion to the
         respective amounts of dividends accumulated and unpaid on the Senior
         Preferred Stock and accumulated and unpaid on such Parity Securities.

                 (e)  So long as any shares of the Senior Preferred Stock are
         outstanding, no dividends (other than dividends or distributions paid
         in shares of, or options, warrants or rights to subscribe for or
         purchase shares of, Junior Securities) shall be declared or paid or
         set apart for payment or other distribution declared or made upon
         Junior Securities, nor shall any Junior Securities be redeemed,
         purchased or otherwise acquired (other than a redemption, purchase or
         other acquisition of shares of Common Stock made for purposes of an
         employee incentive or benefit plan of the Corporation or any
         subsidiary) (all such dividends, distributions,





                                       6
<PAGE>   7
         redemptions or purchases being hereinafter referred to as a "JUNIOR
         SECURITIES DISTRIBUTION") for any consideration (or any moneys be paid
         to or made available for a sinking fund for the redemption of any
         shares of any such stock) by the Corporation, directly or indirectly
         (except by conversion into or exchange for Junior Securities), unless
         in each case (i) the full cumulative dividends on all outstanding
         shares of the Senior Preferred Stock and any other Parity Securities
         shall (to the extent payable in cash) have been paid or set apart for
         payment for all past Dividend Periods with respect to the Senior
         Preferred Stock and all past dividend periods with respect to such
         Parity Securities and (ii) (to the extent payable in cash) sufficient
         funds shall have been paid or set apart for the payment of the
         dividend for the current Dividend Period with respect to the Senior
         Preferred Stock and the current dividend period with respect to such
         Parity Securities.

                 (4) LIQUIDATION PREFERENCE. (a)  In the event of any
         liquidation, dissolution or winding up of the Corporation, whether
         voluntary or involuntary, before any payment or distribution of the
         assets of the Corporation (whether capital or surplus) shall be made
         to or set apart for the holders of Junior Securities, the holders of
         the shares of Senior Preferred Stock shall be entitled to receive an
         amount equal to the Liquidation Value of such share plus any accrued
         and unpaid cash dividends to the date of distribution.  "LIQUIDATION
         VALUE" on any date means, with respect to (x) any share of Senior
         Preferred Stock other than any Additional Shares, the sum of (1)
         $25.00 per share and (2) the aggregate of all dividends accreted on
         such share until the most recent Dividend Payment Date upon which an
         accretion to Liquidation Value has occurred (or if such date is a
         Dividend Payment Date upon which an accretion to Liquidation Value has
         occurred, such date), provided that in the event of an actual
         liquidation, dissolution or winding up of the Corporation or the
         redemption of any shares of Senior Preferred Stock pursuant to Section
         5 hereunder,  the amount referred to in (2) shall be calculated by
         including dividends accreting to the actual date of such liquidation,
         dissolution or winding up or the redemption date, as the case may be,
         rather than the Dividend Payment Date referred to above and provided
         further that in no event will dividends accrete beyond the earlier of
         (i) the Cash Pay Date and (ii) the most recent Dividend Payment Date
         prior to the Dividend Payment Date on which dividends on the Senior
         Preferred Stock are payable in Additional Shares and (y) any
         Additional Share, the Applicable Liquidation Value. All accretions





                                       7
<PAGE>   8
         to Liquidation Value will be calculated using compounding on a
         quarterly basis. Except as provided in the preceding sentences,
         holders of shares of Senior Preferred Stock shall not be entitled to
         any distribution in the event of liquidation, dissolution or winding
         up of the affairs of the Corporation. If, upon any liquidation,
         dissolution or winding up of the Corporation, the assets of the
         Corporation, or proceeds thereof, distributable among the holders of
         the shares of Senior Preferred Stock shall be insufficient to pay in
         full the preferential amount aforesaid and liquidating payments on any
         Parity Securities, then such assets, or the proceeds thereof, shall be
         distributed among the holders of shares of Senior Preferred Stock and
         any such other Parity Securities ratably in accordance with the
         respective amounts that would be payable on such shares of Senior
         Preferred Stock and any such other stock if all amounts payable
         thereon were paid in full. For the purposes of this Section 4, (i) a
         consolidation or merger of the Corporation with one or more
         corporations, or (ii) a sale or transfer of all or substantially all
         of the Corporation's assets, shall not be deemed to be a liquidation,
         dissolution or winding up, voluntary or involuntary, of the
         Corporation.

                 (b) Subject to the rights of the holders of any Parity
         Securities, after payment shall have been made in full to the holders
         of the Senior Preferred Stock, as provided in this paragraph (4), any
         other series or class or classes of Junior Securities shall, subject
         to the respective terms and provisions (if any) applying thereto, be
         entitled to receive any and all assets remaining to be paid or
         distributed, and the holders of the Senior Preferred Stock shall not
         be entitled to share therein.

                 (c) The Applicable Liquidation Value of any Additional Shares
         shall be the Liquidation Value of Senior Preferred Stock outstanding
         immediately prior to the first Dividend Payment Date occurring after a
         request for payment in Additional Shares has been made in accordance
         with Section 3(b).

                 (5) REDEMPTION. (a)  Redemption Upon Consummation of Public
         Offering. The Corporation may, at its option, to the extent it shall
         have funds legally available for such payment, redeem, prior to May
         15, 2001, in whole but not in part, shares of Senior Preferred Stock,
         at a redemption price per share equal to 113% of the Liquidation
         Value, in cash, plus accrued and unpaid cash dividends on such shares
         to the date fixed for redemption, without interest,





                                       8
<PAGE>   9
         provided that the Corporation shall not redeem any shares of Senior
         Preferred Stock pursuant to this Section 5(a) unless (i) prior to such
         redemption a Public Offering shall have been consummated, and (ii) the
         aggregate redemption price of the shares of Senior Preferred Stock
         redeemed pursuant to this Section 5(a) does not exceed the net
         proceeds received by the Corporation in such Initial Public Offering.

                 "PUBLIC OFFERING" shall mean any underwritten public offering
         of Common Stock pursuant to an effective registration statement under
         the Securities Act of 1933, as amended, and shall, in addition, for
         the purposes of Section 5(a) hereof, include any sale, pursuant to
         such an underwritten registered public offering, following the Closing
         Date of any common stock by any affiliate of the Corporation, the net
         proceeds of which are contributed or loaned to the Corporation in such
         a manner that such proceeds may lawfully be used for the redemption of
         the Senior Preferred Stock.

                 "CLOSING DATE" shall have the meaning ascribed to such term in
         the Investors' Agreement.

                 "INVESTORS' AGREEMENT" means the Investors' Agreement dated
         May 22, 1998, among Thermadyne Holdings Corporation, DLJ Merchant
         Banking Partners II, L.P., DLJ Merchant Banking Partners II-A, L.P.,
         DLJ Offshore Partners, C.V., DLJ Merchant Banking Funding, Inc., DLJ
         Offshore Partners II, C.V., DLJ Diversified Partners, L.P., DLJ
         Diversified Partners-A, L.P., DLJ Millennium Partners, L.P., DLJ
         Millennium-A, L.P., DLJMB Funding II, Inc., DLJ EAB Partners, L.P.,
         DLJ First ESC L.P., UK Investment Plan 1997 Partners, DLJ ESC II, L.P.
         (collectively, the "DLJMB Funds"), and certain other stockholders
         listed on the signature pages thereof.

                 (b) Redemption At the Option of the Corporation. On and after
         May 15, 2003, to the extent the Corporation shall have funds legally
         available for such payment, the Corporation may, at its option, redeem
         shares of Senior Preferred Stock, at any time in whole but not in
         part, at redemption prices per share in cash set forth in the table
         below, together with accrued and unpaid cash dividends thereon to the
         date fixed for redemption, without interest:





                                       9
<PAGE>   10
<TABLE>
<CAPTION>
                            Twelve Months Beginning
                                     May 15,                        Percentage of Liquidation Value
                                     -------                        -------------------------------
                                      <S>                                      <C>
                                      2003                                     106.500%
                                      2004                                     104.333
                                      2005                                     102.167

                                      2006                                     100.000
</TABLE>


                 (c) Redemption In the Event of a Change of Control. In the
         event of a Change of Control, the Corporation shall, to the extent it
         shall have funds legally available for such payment, offer to redeem
         all of the shares of Senior Preferred Stock then outstanding, and
         shall redeem the shares of Senior Preferred Stock of any holder of
         such shares that shall consent to such redemption, upon a date no
         later than 30 days following the Change in Control, at a redemption
         price per share equal to 101% of the Liquidation Value, in cash, plus
         accrued and unpaid cash dividends thereon to the date fixed for
         redemption, without interest.

                 "CHANGE OF CONTROL" means such time as: (a) a "person" or
         "group" (within the meaning of Sections 13(d) and 14(d)(2) of the
         Securities Exchange Act of 1934, as amended), other than any person or
         group comprised solely of the Initial Investors, has become the
         beneficial owner, by way of merger, consolidation or otherwise, of 30%
         or more of the voting power of all classes of voting securities of the
         Corporation, and such person or group has become the beneficial owner
         of a greater percentage of the voting power of all classes of voting
         securities of the Corporation than that beneficially owned by the
         Initial Investors; or (b) a sale or transfer of all or substantially
         all of the assets of the Corporation to any person or group (other
         than any group consisting solely of the Initial Investors or their
         affiliates) has been consummated; or (c) during any period of two
         consecutive years, individuals who at the beginning of such period
         constituted the Board of Directors of the Corporation (together with
         any new directors whose election was approved by a vote of a majority
         of the directors then still in office, who either were directors at
         the beginning of such period or whose election or nomination for the
         election was previously so approved) cease for any reason to
         constitute a majority of the directors of the Corporation, then in
         office.





                                       10
<PAGE>   11
                 "INITIAL INVESTORS" means the Stockholders (determined as of
         the issuance of the Preferred Stock) and their Permitted Transferees,
         each as defined in the Investors' Agreement.

                 (d) Mandatory Redemption. To the extent the Corporation shall
         have funds legally available for such payment, on May 15, 2010, if any
         shares of the Senior Preferred Stock shall be outstanding, the
         Corporation shall redeem all outstanding shares of the Senior
         Preferred Stock, at a redemption price equal to the aggregate
         Liquidation Value, in cash, together with any accrued and unpaid cash
         dividends thereon to the date fixed for redemption, without interest.

                 (e) Status of Redeemed Shares. Shares of Senior Preferred
         Stock which have been issued and reacquired in any manner, including
         shares purchased or redeemed, shall (upon compliance with any
         applicable provisions of the laws of the State of Delaware) have the
         status of authorized and unissued shares of the class of Preferred
         Stock undesignated as to series and may be redesignated and reissued
         as part of any series of the Preferred Stock; provided that no such
         issued and reacquired shares of Senior Preferred Stock shall be
         reissued or sold as Senior Preferred Stock.

                 (f) Failure to Redeem. If the Corporation is unable or shall
         fail to discharge its obligation to redeem all outstanding shares of
         Senior Preferred Stock pursuant to paragraph (5)(c) or 5(d) (each, a
         "MANDATORY REDEMPTION OBLIGATION"), such Mandatory Redemption
         Obligation shall be discharged as soon as the Corporation is able to
         discharge such Mandatory Redemption Obligation. If and so long as any
         Mandatory Redemption Obligation with respect to the Senior Preferred
         Stock shall not be fully discharged, the Corporation shall not (i)
         directly or indirectly, redeem, purchase, or otherwise acquire any
         Parity Security or discharge any mandatory or optional redemption,
         sinking fund or other similar obligation in respect of any Parity
         Securities (except in connection with a redemption, sinking fund or
         other similar obligation to be satisfied pro rata with the Senior
         Preferred Stock) or (ii) in accordance with paragraph 3(e), declare or
         make any Junior Securities Distribution, or, directly or indirectly,
         discharge any mandatory or optional redemption, sinking fund or other
         similar obligation in respect of the Junior Securities.





                                       11
<PAGE>   12
                 (g) Failure to Pay Dividends. Notwithstanding the foregoing
         provisions of this paragraph (5), unless full cumulative cash
         dividends (whether or not declared) on all outstanding shares of
         Senior Preferred Stock shall have been paid or contemporaneously are
         declared and paid or set apart for payment for all dividend periods
         terminating on or prior to the applicable redemption date, none of the
         shares of Senior Preferred Stock shall be redeemed, and no sum shall
         be set aside for such redemption, unless shares of Senior Preferred
         Stock are redeemed pro rata.

                 (6) PROCEDURE FOR REDEMPTION. (a) In the event the Corporation
         shall redeem shares of Senior Preferred Stock pursuant to Sections
         5(a), (b) or (d), notice of such redemption shall be given by first
         class mail, postage prepaid, mailed not less than 30 days nor more
         than 60 days prior to the redemption date, to each holder of record of
         the shares to be redeemed at such holder's address as the same appears
         on the stock register of the Corporation; provided that neither the
         failure to give such notice nor any defect therein shall affect the
         validity of the giving of notice for the redemption of any share of
         Senior Preferred Stock to be redeemed except as to the holder to whom
         the Corporation has failed to give said notice or except as to the
         holder whose notice was defective. Each such notice shall state: (i)
         the redemption date; (ii) the number of shares of Senior Preferred
         Stock to be redeemed; (iii) the redemption price; (iv) the place or
         places where certificates for such shares are to be surrendered for
         payment of the redemption price; and (v) that dividends on the shares
         to be redeemed will cease to accrue on such redemption date.

                 (b)  In the case of any redemption pursuant to Sections 5(a),
         (b) or (d) hereof, notice having been mailed as provided in Section
         6(a) hereof, from and after the redemption date (unless default shall
         be made by the Corporation in providing money for the payment of the
         redemption price of the shares called for redemption), dividends on
         the shares of Senior Preferred Stock so called for redemption shall
         cease to accrue, and all rights of the holders thereof as stockholders
         of the Corporation (except the right to receive from the Corporation
         the redemption price) shall cease. Upon surrender in accordance with
         said notice of the certificates for any shares so redeemed (properly
         endorsed or assigned for transfer, if the Board of Directors of the
         Corporation shall so require and the notice shall so state), such
         share shall be redeemed by the Corporation at the redemption price
         aforesaid. In case fewer than all the shares





                                       12
<PAGE>   13
         represented by any such certificate are redeemed, a new certificate
         shall be issued representing the unredeemed shares without cost to the
         holder thereof.

                 (c)  In the case of a redemption pursuant to Section 5(c)
         hereof, notice of such redemption shall be given by first class mail,
         postage prepaid, mailed not more than 10 days following the occurrence
         of the Change of Control and not less than 20 days prior to the
         redemption date, to each holder of record of the shares to be redeemed
         at such holder's address as the same appears on the stock register of
         the Corporation; provided that neither the failure to give such notice
         nor any defect therein shall affect the validity of the giving of
         notice for the redemption of any share of Senior Preferred Stock to be
         redeemed except as to the holder to whom the Corporation has failed to
         give said notice or except as to the holder whose notice was
         defective. Each such notice shall state: (i) that a Change of Control
         has occurred; (ii) the redemption date; (iii) the redemption price;
         (iv) that such holder may elect to cause the Corporation to redeem all
         or any of the shares of Senior Preferred Stock held by such holder;
         (v) the place or places where certificates for such shares are to be
         surrendered for payment of the redemption price; and (vi) that
         dividends on the shares the holder elects to cause the Corporation to
         redeem will cease to accrue on such redemption date.

                 Upon receipt of such notice, the holder shall, within 20 days
         of receipt thereof, return such notice to the Corporation indicating
         the number of shares of Senior Preferred Stock such holder shall elect
         to cause the Corporation to redeem, if any.

                 (d)  In the case of a redemption pursuant to Section 5(c)
         hereof, notice having been mailed as provided in Section 6(c) hereof,
         from and after the redemption date (unless default shall be made by
         the Corporation in providing money for the payment of the redemption
         price of the shares called for redemption), dividends on such shares
         of Senior Preferred Stock as the holder elects to cause the
         Corporation to redeem shall cease to accrue, and all rights of the
         holders thereof as stockholders of the Corporation (except the right
         to receive from the Corporation the redemption price) shall cease.
         Upon surrender in accordance with said notice of the certificates for
         any shares so redeemed (properly endorsed or assigned for transfer, if
         the Board of Directors of the Corporation shall so require and the
         notice shall so state), such share shall be





                                       13
<PAGE>   14
         redeemed by the Corporation at the redemption price aforesaid. In case
         fewer than all the shares represented by any such certificate are
         redeemed, a new certificate shall be issued representing the
         unredeemed shares without cost to the holder thereof.

                 (7) EXCHANGE. (a) Subject to the provisions of this paragraph
         (7) the Corporation may, at its option, at any time and from time to
         time on any Dividend Payment Date, exchange, to the extent it is
         legally permitted to do so, all, but not less than all, outstanding
         shares (and fractional shares) of Senior Preferred Stock, for Exchange
         Debentures, provided that (i) on or prior to the date of exchange the
         Corporation shall have paid to or declared and set aside for payment
         to the holders of outstanding shares of Senior Preferred Stock all
         accrued and unpaid cash dividends on shares of Senior Preferred Stock
         through the exchange date in accordance with the next succeeding
         paragraph; (ii) no event of default under the indenture (as defined in
         such indenture) governing the Exchange Debentures shall have occurred
         and be continuing; and (iii) no shares of Senior Preferred Stock are
         held on such date by the DLJMB Funds or any of their Affiliates, or
         any of their Permitted Transferees.  The principal amount of Exchange
         Debentures deliverable upon exchange of a share of Senior Preferred
         Stock, adjusted as hereinafter provided, shall be determined in
         accordance with the Exchange Ratio (as defined below).

                 Cash dividends on any shares of Senior Preferred Stock
         exchanged for Exchange Debentures which have accrued but have not been
         paid as of the date of exchange shall be paid in cash.  In no event
         shall the Corporation issue Exchange Debentures in denominations other
         than $1,000 or in an integral multiple thereof.  Cash will be paid in
         lieu of any such fraction of an Exchange Debenture which would
         otherwise have been issued (which shall be determined with respect to
         the aggregate principal amount of Exchange Debentures to be issued to
         a holder upon any such exchange). Interest will accrue on the Exchange
         Debentures from the date of exchange.

                 Prior to effecting any exchange hereunder, the Corporation
         shall appoint a trustee to serve in the capacity contemplated by an
         indenture between the Corporation and such trustee,  containing
         customary terms and conditions.





                                       14
<PAGE>   15
                 The EXCHANGE RATIO shall be, as of any Dividend Payment Date,
         $1.00 (or fraction thereof) of principal amount of Exchange Debenture
         for each $1.00 of (i) Liquidation Value plus (ii) accrued and unpaid
         cash dividends, if any, per share of Senior Preferred Stock held by a
         holder on the applicable exchange date.

                 "AFFILIATES" shall have the meaning ascribed to such term in
         the Investors' Agreement.

                 "EXCHANGE DEBENTURES" means 13%  Subordinated Exchange
         Debentures due 2010 of the Corporation, to be issued pursuant to an
         indenture between the Corporation and a trustee, containing customary
         terms and conditions, in accordance with the Term Sheet attached as
         Exhibit A hereto.

                 "PERMITTED TRANSFEREES" shall have the meaning ascribed to
         such term in the Investors' Agreement.

                          (b) Procedure for Exchange. (i) In the event the
         Corporation shall exchange shares of Senior Preferred Stock, notice of
         such exchange shall be given by first class mail, postage prepaid,
         mailed not less than 30 days nor more than 60 days prior to the
         exchange date, to each holder of record of the shares to be exchanged
         at such holder's address as the same appears on the stock register of
         the Corporation; provided that neither the failure to give such notice
         nor any defect therein shall affect the validity of the giving of
         notice for the exchange of any share of Senior Preferred Stock to be
         exchanged except as to the holder to whom the Corporation has failed
         to give said notice or except as to the holder whose notice was
         defective. Each such notice shall state: (A) the exchange date; (B)
         the number of shares of Senior Preferred Stock to be exchanged; (C)
         the Exchange Ratio; (D) the place or places where certificates for
         such shares are to be exchanged for notes evidencing the Exchange
         Debentures to be received by the exchanging holder; and (E) that
         dividends on the shares to be exchanged will cease to accrue on such
         exchange date.

                          (ii) Prior to giving notice of intention to exchange,
                          the Corporation shall execute and deliver to a bank or
                          trust company selected by the Corporation an indenture
                          containing customary terms and conditions. The
                          Corporation will cause the Exchange Debentures to be
                          authenticated on the





                                       15
<PAGE>   16
                 Dividend Payment Date on which the exchange is effective, and
                 will pay interest on the Exchange Debentures at the rate and
                 on the dates specified in such indenture from the exchange
                 date.

                          The Corporation will not give notice of its intention
                 to exchange under paragraph 6(b)(i) hereof unless it shall
                 file at the place or places (including a place in the Borough
                 of Manhattan, The City of New York) maintained for such
                 purpose an opinion of counsel (who may be an employee of the
                 Corporation) to the effect that (i) the indenture has been
                 duly authorized, executed and delivered by the Corporation,
                 has been duly qualified under the Trust Indenture Act of 1939
                 (or that such qualification is not necessary) and constitutes
                 a valid and binding instrument enforceable against the
                 Corporation in accordance with its terms (subject, as to
                 enforcement, to bankruptcy, insolvency, reorganization and
                 other laws of general applicability relating to or affecting
                 creditors' rights and to general equity principles, and
                 subject to such other qualifications as are then customarily
                 contained in opinions of counsel experienced in such matters),
                 (ii) the Exchange Debentures have been duly authorized and,
                 when executed and authenticated in accordance with the
                 provisions of the indenture and delivered in exchange for the
                 shares of Preferred Stock, will constitute valid and binding
                 obligations of the Corporation entitled to the benefits of the
                 indenture (subject as aforesaid), (iii) neither the execution
                 nor delivery of the indenture or the Exchange Debentures nor
                 compliance with the terms, conditions or provisions of such
                 instruments will result in a breach or violation of any of the
                 terms or provisions of, or constitute a default under, any
                 indenture, mortgage, deed of trust or agreement or instrument,
                 known to such counsel, to which the Corporation or any of its
                 subsidiaries is a party or by which it or any of them is
                 bound, or any decree, judgment, order, rule or regulation,
                 known to such counsel, of any court or governmental agency or
                 body having jurisdiction over the Corporation and





                                       16
<PAGE>   17
                          such subsidiaries or any of their properties, (iv) the
                          Exchange Debentures have been duly registered for such
                          exchange with the Securities and Exchange Commission
                          under a registration statement that has become
                          effective under the Securities Act of 1933 (the "Act")
                          or that the exchange of the Exchange Debentures for
                          the shares of Senior Preferred Stock is exempt from
                          registration under the Act, and (v) the Corporation
                          has sufficient legally available funds for such
                          exchange such that such exchange is permitted under
                          applicable law.

                          (iii)  Notice having been mailed as aforesaid, from
                          and after the exchange date (unless default shall be
                          made by the Corporation in issuing Exchange Debentures
                          in exchange for the shares called for exchange),
                          dividends on the shares of Senior Preferred Stock so
                          called for exchange shall cease to accrue, and all
                          rights of the holders thereof as stockholders of the
                          Corporation (except the right to receive from the
                          Corporation the Exchange Debentures and any rights
                          such holder, upon the exchange, may have as a holder
                          of the Exchange Debenture) shall cease. Upon surrender
                          in accordance with said notice of the certificates for
                          any shares so exchanged (properly endorsed or assigned
                          for transfer, if the Board of Directors of the
                          Corporation shall so require and the notice shall so
                          state), such share shall be exchanged by the
                          Corporation for the Exchange Debentures at the
                          Exchange Ratio. In case fewer than all the shares
                          represented by any such certificate are exchanged, a
                          new certificate shall be issued representing the
                          unexchanged shares without cost to the holder thereof.

                          (iv)   Each exchange shall be deemed to have been
                          effected immediately after the close of business on
                          the relevant Dividend Payment Date, and the person in
                          whose name or names any Exchange Debentures shall be
                          issuable upon such exchange shall be deemed to have
                          become the holder of record of the





                                       17
<PAGE>   18
                          Exchange Debentures represented thereby at such time
                          on such Dividend Payment Date.

                          (v)  Prior to the delivery of any securities which the
                          Corporation shall be obligated to deliver upon
                          exchange of the Senior Preferred Stock, the
                          Corporation shall comply with all applicable federal
                          and state laws and regulations which require action to
                          be taken by the Corporation.

                 (c) The Corporation will pay any and all documentary stamp or
         similar issue or transfer taxes payable in respect of the issue or
         delivery of notes evidencing Exchange Debentures on exchange of the
         Senior Preferred Stock pursuant hereto; provided that the Corporation
         shall not be required to pay any tax which may be payable in respect
         of any transfer involved in the issue or delivery of Exchange
         Debentures in a name other than that of the holder of the Senior
         Preferred Stock to be exchanged and no such issue or delivery shall be
         made unless and until the person requesting such issue or delivery has
         paid to the Corporation the amount of any such tax or has established,
         to the satisfaction of the Corporation, that such tax has been paid.

                          (8) VOTING RIGHTS. (a)  The holders of record of
         shares of Senior Preferred Stock shall not be entitled to any voting
         rights except as hereinafter provided in this paragraph (8), as
         otherwise provided by law or as provided in the Investors' Agreement.

                          (b) If and whenever (i) four consecutive or six
         quarterly cash dividends payable on the Senior Preferred Stock have not
         been paid in full, (ii) for any reason (including the reason that funds
         are not legally available for a redemption), the Corporation shall have
         failed to discharge any Mandatory Redemption Obligation (including a
         redemption in the Event of a Change of Control pursuant to Section 5(c)
         hereof), (iii) the Corporation shall have failed to provide the notice
         required by Section 6(c) hereof within the time period specified in
         such section or (iv) the Corporation shall have failed to comply with
         Sections 3(d), 3(e) or 8(c) hereof, (1) the number of directors then
         constituting the Board of Directors shall be increased by two and the
         holders of a majority of the outstanding shares of Senior Preferred
         Stock, together with the holders of shares of every other





                                       18
<PAGE>   19
         series of preferred stock upon which like rights have been conferred
         and are exercisable (resulting from either the failure to pay
         dividends or the failure to redeem) (any such series is referred to as
         the "PREFERRED SHARES"), voting as a single class regardless of
         series, shall be entitled to elect the two additional directors to
         serve on the Board of Directors at any annual meeting of stockholders
         or special meeting held in place thereof, or at a special meeting of
         the holders of the Senior Preferred Stock and the Preferred Shares
         called as hereinafter provided. Whenever (i) all arrears in cash
         dividends on the Senior Preferred Stock and the Preferred Shares then
         outstanding shall have been paid and cash dividends thereon for the
         current quarterly dividend period shall have been paid or declared and
         set apart for payment, (ii) the Corporation shall have fulfilled its
         Mandatory Redemption Obligation, (iii) fulfilled its obligation to
         provide notice as specified in subsection (b)(iii) hereof, or (iv) the
         Corporation shall have complied with Sections 3(d), 3(e), or 8(c)
         hereof, as the case may be, then the right of the holders of the
         Senior Preferred Stock to elect such additional two directors shall
         cease (but subject always to the same provisions for the vesting of
         such voting rights in the case of any similar future (i) arrearage in
         six consecutive quarterly cash dividends, (ii) failure to fulfill any
         Mandatory Redemption Obligation, (iii) failure to fulfill the
         obligation to provide the notice required by Section 6(d) hereof
         within the time period specified in such section or (iv) failure to
         comply with Sections 3(d), 3(e), or 8(c)) and the terms of office of
         all persons elected as directors by the holders of the Senior
         Preferred Stock shall forthwith terminate and the number of the Board
         of Directors shall be reduced accordingly. At any time after such
         voting power shall have been so vested in the holders of shares of
         Senior Preferred Stock and the Preferred Shares, the secretary of the
         Corporation may, and upon the written request of any holder of Senior
         Preferred Stock (addressed to the secretary at the principal office of
         the Corporation) shall, call a special meeting of the holders of the
         Senior Preferred Stock and of the Preferred Shares for the election of
         the two directors to be elected by them as herein provided, such call
         to be made by notice similar to that provided in the Bylaws of the
         Corporation for a special meeting of the stockholders or as required
         by law. If any such special meeting required to be called as above
         provided shall not be called by the secretary within 20 days after
         receipt of any such request, then any holder of shares of Senior
         Preferred Stock may call such meeting, upon the notice above provided,
         and for that purpose shall have access to the stock books of the
         Corporation. The directors elected





                                       19
<PAGE>   20
         at any such special meeting shall hold office until the next annual
         meeting of the stockholders or special meeting held in lieu thereof if
         such office shall not have previously terminated as above provided. If
         any vacancy shall occur among the directors elected by the holders of
         the Senior Preferred Stock and the Preferred Shares, a successor shall
         be elected by the Board of Directors, upon the nomination of the
         then-remaining director elected by the holders of the Senior Preferred
         Stock and the Preferred Shares or the successor of such remaining
         director, to serve until the next annual meeting of the stockholders
         or special meeting held in place thereof if such office shall not have
         previously terminated as provided above.

                 (c) Without the written consent of a majority of the
         outstanding shares of Senior Preferred Stock or the vote of holders of
         a majority of the outstanding shares of Senior Preferred Stock at a
         meeting of the holders of Senior Preferred Stock called for such
         purpose, the Corporation will not (i) amend, alter or repeal any
         provision of the Certificate of Incorporation (by merger or otherwise)
         so as to adversely affect the preferences, rights or powers of the
         Senior Preferred Stock; provided that any such amendment that
         decreases the dividend payable on or the Liquidation Value of the
         Senior Preferred Stock shall require the affirmative vote of holders
         of each share of Senior Preferred Stock at a meeting of holders of
         Senior Preferred Stock called for such purpose or written consent of
         the holder of each share of Senior Preferred Stock; or (ii) create,
         authorize or issue any class of stock ranking prior to, or on a parity
         with, the Senior Preferred Stock with respect to dividends or upon
         liquidation, dissolution, winding up or otherwise, or increase the
         authorized number of shares of any such class or series, or reclassify
         any authorized stock of the Corporation into any such prior or parity
         shares or create, authorize or issue any obligation or security
         convertible into or evidencing the right to purchase any such prior or
         parity shares, except that the Corporation may, without such approval,
         create authorize and issue Parity Securities for the purpose of
         utilizing the proceeds from the issuance of such Parity Securities for
         the redemption or repurchase of all outstanding shares of Senior
         Preferred Stock in accordance with the terms hereof or of the
         Investors' Agreement.

                 (d) In exercising the voting rights set forth in this
         paragraph (8), each share of Senior Preferred Stock shall have one
         vote per share, except that when any other series of preferred stock
         shall





                                       20
<PAGE>   21
         have the right to vote with the Senior Preferred Stock as a single
         class on any matter, then the Senior Preferred Stock and such other
         series shall have with respect to such matters one vote per $25 of
         Liquidation Value or other liquidation preference. Except as otherwise
         required by applicable law or as set forth herein, the shares of
         Senior Preferred Stock shall not have any relative, participating,
         optional or other special voting rights and powers and the consent of
         the holders thereof shall not be required for the taking of any
         corporate action.

                 (9) REPORTS. So long as any of the Senior Preferred Stock is
         outstanding, the Corporation will furnish the holders thereof with the
         quarterly and annual financial reports that the Corporation is
         required to file with the Securities and Exchange Commission pursuant
         to Section 13 or Section 15(d) of the Securities Exchange Act of 1934
         or, in the event the Corporation is not required to file such reports,
         reports containing the same information as would be required in such
         reports.

                 (10) GENERAL PROVISIONS. (a)  The term "PERSON" as used herein
         means any corporation, limited liability company, partnership, trust,
         organization, association, other entity or individual.

                 (b)      The term "OUTSTANDING," when used with reference to
         shares of stock, shall mean issued shares, excluding shares held by
         the Corporation or a subsidiary.

                 (c)      The headings of the paragraphs, subparagraphs,
         clauses and subclauses used herein are for convenience of reference
         only and shall not define, limit or affect any of the provisions
         hereof.

                 (d)      Each holder of Senior Preferred Stock, by acceptance
         thereof, acknowledges and agrees that payments of dividends, interest,
         premium and principal on, and exchange, redemption and repurchase of,
         such securities by the Corporation are subject to restrictions on the
         Corporation contained in certain credit and financing agreements.

                 FIFTH:  No contract or transaction between the Corporation and
         one or more of its directors, officers, or stockholders or between the
         Corporation and any person (as used





                                       21
<PAGE>   22
         herein "person" means any other corporation, partnership, association,
         firm, trust, joint venture, political subdivision, or instrumentality)
         or other organization in which one or more of its directors, officers,
         or stockholders are directors, officers or stockholders, or have a
         financial interest, shall be void or voidable solely for this reason,
         or solely because the director or officer is present at or
         participates in the meeting of the board or committee which authorizes
         the contract or transaction, or solely because his, her, or their
         votes are counted for such purpose, if: (i) the material facts as to
         his or her relationship or interest and as to the contract or
         transaction are disclosed or are known to the board of directors or
         the committee, and the board of directors or committee in good faith
         authorizes the contract or transaction by the affirmative votes of a
         majority of the disinterested directors, even though the disinterested
         directors be less than a quorum; or (ii) the material facts as to his
         or her relationship or interest and as to the contract or transaction
         are disclosed or are known to the stockholders entitled to vote
         thereon, and the contract or transaction is specifically approved in
         good faith by vote of the stockholders; or (iii) the contract or
         transaction is fair as to the Corporation as of the time it is
         authorized, approved, or ratified by the board of directors, a
         committee thereof (to the extent permitted by applicable law), or the
         stockholders.  Common or interested directors may be counted in
         determining the presence of a quorum at a meeting of the board of
         directors or of a committee which authorizes the contract or
         transaction.

                 SIXTH: The Board of Directors shall have the power to adopt,
         amend or repeal the bylaws of the Corporation.

                 SEVENTH: Election of directors need not be by written ballot
         unless the bylaws of the Corporation so provide.

                 EIGHTH:  A director of the Corporation shall not be personally
         liable to the Corporation or its stockholders for monetary damages for
         breach of fiduciary duty as a director, except for liability (i) for
         any breach of the director's duty of loyalty to the Corporation or its
         stockholders, (ii) for acts or omissions not in good faith or which
         involve intentional misconduct or knowing violation of law, (iii)
         under Section 174 of the Delaware Law, or (iv) for any transaction
         from which the director derived an improper personal benefit.  Any
         repeal or amendment of this Article EIGHTH by the stockholders of the
         Corporation shall be prospective only,





                                       22
<PAGE>   23
         and shall not adversely affect any limitation on the personal
         liability of a director of the Corporation arising from an act or
         omission occurring prior to the time of such repeal or amendment.  In
         addition to the circumstances in which a director of the Corporation
         is not personally liable as set forth in the foregoing provisions of
         this Article EIGHTH, a director shall not be liable to the Corporation
         or its stockholders to such further extent as permitted by any law
         hereafter enacted, including without limitation any subsequent
         amendment to the Delaware Law.

                 NINTH: (1) A director of the Corporation shall not be liable
         to the Corporation or its stockholders for monetary damages for breach
         of fiduciary duty as a director to the fullest extent permitted by
         Delaware Law.

                 (2)(a) Each person (and the heirs, executors or administrators
         of such person) who was or is a party or is threatened to be made a
         party to, or is involved in any threatened, pending or completed
         action, suit or proceeding, whether civil, criminal, administrative or
         investigative, by reason of the fact that such person is or was a
         director or officer of the Corporation or is or was serving at the
         request of the Corporation as a director or officer of another
         corporation, partnership, joint venture, trust or other enterprise,
         shall be indemnified and held harmless by the Corporation to the
         fullest extent permitted by Delaware Law.  The right to
         indemnification conferred in this Article NINTH shall also include the
         right to be paid by the Corporation the expenses incurred in
         connection with any such proceeding in advance of its final
         disposition to the fullest extent authorized by Delaware Law.  The
         right to indemnification conferred in this Article NINTH shall be a
         contract right.

                 (b) The Corporation may, by action of its Board of Directors,
         provide indemnification to such of the officers, employees and agents
         of the Corporation to such extent and to such effect as the Board of
         Directors shall determine to be appropriate and authorized by Delaware
         Law.

                 (3) The Corporation shall have power to purchase and maintain
         insurance on behalf of any person who is or was a director, officer,
         employee or agent of the Corporation, or is or was serving at the
         request of the Corporation as a director, officer, employee or agent
         of another corporation, partnership, joint





                                       23
<PAGE>   24
         venture, trust or other enterprise against any expense, liability or
         loss incurred by such person in any such capacity or arising out of
         his status as such, whether or not the Corporation would have the
         power to indemnify him against such liability under Delaware Law.

                 (4) The rights and authority conferred in this Article NINTH
         shall not be exclusive of any other right which any person may
         otherwise have or hereafter acquire.

                 (5) Neither the amendment nor repeal of this Article NINTH,
         nor the adoption of any provision of this Certificate of Incorporation
         or the bylaws of the Corporation, nor, to the fullest extent permitted
         by Delaware Law, any modification of law, shall eliminate or reduce
         the effect of this Article NINTH in respect of any acts or omissions
         occurring prior to such amendment, repeal, adoption or modification.

                 TENTH:  The Corporation expressly elects not to be governed by
         Section 203 of the Delaware Law.

                 ELEVENTH: The Corporation reserves the right to amend this
         Certificate of Incorporation in any manner permitted by Delaware Law
         and, with the sole exception of those rights and powers conferred
         under the above Article NINTH, all rights and powers conferred herein
         on stockholders, directors and officers, if any, are subject to this
         reserved power.





                                       24
<PAGE>   25
                                                                       EXHIBIT A


                                SUMMARY OF TERMS
                                OF INDENTURE FOR
                      13% SUBORDINATED EXCHANGE DEBENTURES


<TABLE>
 <S>                              <C>
 PARTIES:                          Thermadyne Holdings Corporation (the "CORPORATION") and
                                   [            ], as trustee.

 ISSUE:                            13% Exchange Debentures (the "EXCHANGE DEBENTURES") to
                                   be issued by the Corporation, at its option, in exchange
                                   for any or all the outstanding shares of 13% Senior
                                   Exchangeable Preferred Stock due 2010 (the "SENIOR
                                   PREFERRED STOCK") issued on or about May 15, 1998 to DLJ
                                   Merchant Banking Partners II, L.P. and certain of its
                                   affiliates (the "DLJ ENTITIES").

 MATURITY:                         May 15, 2010.
 INTEREST:                         13% annual rate, payable semi-annually.  Through the
                                   semi-annual interest payment period ending in May 2003,
                                   semi-annual interest will accrete on a compound basis
                                   (i.e. non-cash pay) and increase the face amount of the
                                   Exchange Debentures, thereafter interest will be payable
                                   in cash.

 RANKING:                          The Exchange Debentures will rank senior to all other
                                   subordinated debt, preferred stock and common equity of
                                   the Corporation.


 OPTIONAL REDEMPTION:              The Exchange Debentures will be redeemable at any time
                                   after May 15, 2003 at the option of the Corporation, in
                                   whole or in part, at the same redemption prices set
                                   forth in the designation of the Senior Preferred Stock
                                   set forth in Article FOURTH, paragraph (c) of the
                                   Restated Certificate of Incorporation of the Surviving
                                   Corporation.
</TABLE>





                                       25
<PAGE>   26
<TABLE>
 <S>                <C>            <C>
 CHANGE OF CONTROL  REPURCHASE     In the event of a Change of Control of the Corporation
 RIGHT:                            each holder of the Exchange Debentures will have the
                                   right to require the Corporation to repurchase all or
                                   any part of such holder's Exchange Debentures at a
                                   purchase price of 101% of the sum of the accreted value
                                   thereof plus accrued and unpaid cash interest, if any,
                                   to the repurchase date.

 COVENANTS:                        The Debentures will contain covenants that are
                                   substantially the same as the covenants contained in the
                                   Indenture of the Senior Discount Debentures due 2008 of
                                   the Corporation and will limit, among other things, the
                                   ability of the Corporation and its subsidiaries (i) to
                                   incur additional indebtedness, (ii) to pay dividends and
                                   make other distributions on its capital stock, (iii) to
                                   repurchase its capital stock or warrants, options or
                                   other rights to acquire shares of its capital stock or
                                   any indebtedness subordinated to the Exchange
                                   Debentures, (iv) to make certain other restricted
                                   payments, (v) to make certain investments or asset
                                   sales, (vi) to engage in transactions with affiliates,
                                   (vii) to create liens, (viii) to permit "layering" of
                                   indebtedness and (ix) to merge or consolidate or
                                   transfer all or substantially all of its assets."
</TABLE>


         FIFTH:  The executed Agreement is on file at the office of the
surviving corporation at 101 South Hanley Road, Suite 300, St. Louis, Missouri
63105.

         SIXTH:  A copy of the Agreement will be furnished by the surviving
corporation, on request and without cost, to any stockholder of any constituent
corporation.

         SEVENTH:  This Certificate of Merger shall become effective upon
filing.





                                       26
<PAGE>   27
IN WITNESS WHEREOF, the undersigned has caused this instrument to be duly
executed by its authorized officers.

Dated: May 22, 1998


                                  THERMADYNE HOLDINGS CORPORATION



                                  By:  /s/ STEPHANIE N. JOSEPHSON             
                                       ---------------------------------------
                                          Stephanie N. Josephson
                                          Vice President, Corporate Secretary
                                          and General Counsel





                                       27