<PAGE>   1

                                                                    EXHIBIT 4(a)


                                                                [CONFORMED COPY]
================================================================================

                        TEXAS UTILITIES ELECTRIC COMPANY

                                       TO

                             THE BANK OF NEW YORK,
                        (FORMERLY IRVING TRUST COMPANY)


                                               TRUSTEE UNDER THE TEXAS UTILITIES
                                               ELECTRIC COMPANY MORTGAGE AND
                                               DEED OF TRUST, DATED AS OF
                                               DECEMBER 1, 1983

                                              
                               ------------------

                       FIFTY-SIXTH SUPPLEMENTAL INDENTURE

                        PROVIDING AMONG OTHER THINGS FOR
                            FIRST MORTGAGE BONDS,
                          POLLUTION CONTROL SERIES AC

                                      AND

                             FIRST MORTGAGE BONDS,
                          POLLUTION CONTROL SERIES AD

                               ------------------

                         DATED AS OF SEPTEMBER 1, 1996

================================================================================

            THIS INSTRUMENT GRANTS A SECURITY INTEREST BY A UTILITY
          THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS
<PAGE>   2
            THIS INSTRUMENT GRANTS A SECURITY INTEREST BY A UTILITY
          THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS

                      FIFTY-SIXTH  SUPPLEMENTAL  INDENTURE

                        ----------------------------

       INDENTURE, dated as of September 1, 1996, between TEXAS UTILITIES
ELECTRIC COMPANY, a corporation of the State of Texas, whose address is Energy
Plaza, 1601 Bryan Street, Dallas, Texas 75201 (hereinafter sometimes called the
Company), and THE BANK OF NEW YORK (formerly Irving Trust Company), a
corporation of the State of New York, whose address is 101 Barclay Street, New
York, New York 10286 (hereinafter sometimes called the Trustee), Trustee under
the Mortgage and Deed of Trust, dated as of December 1, 1983 (hereinafter
called the Original Indenture, the Original Indenture and any and all
indentures and instruments supplemental thereto being hereinafter sometimes
collectively called the Mortgage), which Original Indenture was executed and
delivered by the Company to secure the payment of bonds issued or to be issued
under and in accordance with the provisions of the Mortgage, reference to which
Mortgage is made, this Indenture (hereinafter called the Fifty-sixth
Supplemental Indenture) being supplemental thereto;

       WHEREAS, said Original Indenture was recorded or filed as required in
the State of Texas; and

       WHEREAS, the Company executed and delivered to the Trustee the following
supplemental indentures:

<TABLE>
<CAPTION>
                       DESIGNATION                                        DATED AS OF
                       -----------                                        -----------
<S>                                                                       <C>
First Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     April 1, 1984
Second Supplemental Indenture . . . . . . . . . . . . . . . . . . . .     September 1, 1984
Third Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     April 1, 1985
Fourth Supplemental Indenture . . . . . . . . . . . . . . . . . . . .     August 1, 1985
Fifth Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     September 1, 1985
Sixth Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     December 1, 1985
Seventh Supplemental Indenture  . . . . . . . . . . . . . . . . . . .     March 1, 1986
Eighth Supplemental Indenture . . . . . . . . . . . . . . . . . . . .     May 1, 1986
Ninth Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     October 1, 1986
Tenth Supplemental Indenture  . . . . . . . . . . . . . . . . . . . .     December 1, 1986
Eleventh Supplemental Indenture . . . . . . . . . . . . . . . . . . .     December 1, 1986
Twelfth Supplemental Indenture  . . . . . . . . . . . . . . . . . . .     February 1, 1987
Thirteenth Supplemental Indenture . . . . . . . . . . . . . . . . . .     March 1, 1987
Fourteenth Supplemental Indenture . . . . . . . . . . . . . . . . . .     April 1, 1987
Fifteenth Supplemental Indenture  . . . . . . . . . . . . . . . . . .     July 1, 1987
Sixteenth Supplemental Indenture  . . . . . . . . . . . . . . . . . .     September 1, 1987
Seventeenth Supplemental Indenture  . . . . . . . . . . . . . . . . .     October 1, 1987
Eighteenth Supplemental Indenture . . . . . . . . . . . . . . . . . .     March 1, 1988
Nineteenth Supplemental Indenture . . . . . . . . . . . . . . . . . .     May 1, 1988
</TABLE>
<PAGE>   3
                                       2



<TABLE>
<CAPTION>
                       DESIGNATION                                        DATED AS OF
                       -----------                                        -----------
<S>                                                                       <C>
Twentieth Supplemental Indenture  . . . . . . . . . . . . . . . . . .     September 1, 1988
Twenty-first Supplemental Indenture . . . . . . . . . . . . . . . . .     November 1, 1988
Twenty-second Supplemental Indenture  . . . . . . . . . . . . . . . .     January 1, 1989
Twenty-third Supplemental Indenture . . . . . . . . . . . . . . . . .     August 1, 1989
Twenty-fourth Supplemental Indenture  . . . . . . . . . . . . . . . .     November 1, 1989
Twenty-fifth Supplemental Indenture . . . . . . . . . . . . . . . . .     December 1, 1989
Twenty-sixth Supplemental Indenture . . . . . . . . . . . . . . . . .     February 1, 1990
Twenty-seventh Supplemental Indenture . . . . . . . . . . . . . . . .     September 1, 1990
Twenty-eighth Supplemental Indenture  . . . . . . . . . . . . . . . .     October 1, 1990
Twenty-ninth Supplemental Indenture . . . . . . . . . . . . . . . . .     October 1, 1990
Thirtieth Supplemental Indenture  . . . . . . . . . . . . . . . . . .     March 1, 1991
Thirty-first Supplemental Indenture . . . . . . . . . . . . . . . . .     May 1, 1991
Thirty-second Supplemental Indenture  . . . . . . . . . . . . . . . .     July 1, 1991
Thirty-third Supplemental Indenture . . . . . . . . . . . . . . . . .     February 1, 1992
Thirty-fourth Supplemental Indenture  . . . . . . . . . . . . . . . .     April 1, 1992
Thirty-fifth Supplemental Indenture . . . . . . . . . . . . . . . . .     April 1, 1992
Thirty-sixth Supplemental Indenture . . . . . . . . . . . . . . . . .     June 1, 1992
Thirty-seventh Supplemental Indenture . . . . . . . . . . . . . . . .     June 1, 1992
Thirty-eighth Supplemental Indenture  . . . . . . . . . . . . . . . .     August 1, 1992
Thirty-ninth Supplemental Indenture . . . . . . . . . . . . . . . . .     October 1, 1992
Fortieth Supplemental Indenture . . . . . . . . . . . . . . . . . . .     November 1, 1992
Forty-first Supplemental Indenture  . . . . . . . . . . . . . . . . .     December 1, 1992
Forty-second Supplemental Indenture . . . . . . . . . . . . . . . . .     March 1, 1993
Forty-third Supplemental Indenture  . . . . . . . . . . . . . . . . .     April 1, 1993
Forty-fourth Supplemental Indenture . . . . . . . . . . . . . . . . .     April 1, 1993
Forty-fifth Supplemental Indenture  . . . . . . . . . . . . . . . . .     May 1, 1993
Forty-sixth Supplemental Indenture  . . . . . . . . . . . . . . . . .     July 1, 1993
Forty-seventh Supplemental Indenture  . . . . . . . . . . . . . . . .     October 1, 1993
Forty-eighth Supplemental Indenture . . . . . . . . . . . . . . . . .     November 1, 1993
Forty-ninth Supplemental Indenture  . . . . . . . . . . . . . . . . .     May 1, 1994
Fiftieth Supplemental Indenture . . . . . . . . . . . . . . . . . . .     May 1, 1994
Fifty-first Supplemental Indenture  . . . . . . . . . . . . . . . . .     August 1, 1994
Fifty-second Supplemental Indenture . . . . . . . . . . . . . . . . .     April 1, 1995
Fifty-third Supplemental Indenture  . . . . . . . . . . . . . . . . .     June 1, 1995
Fifty-fourth Supplemental Indenture . . . . . . . . . . . . . . . . .     October 1, 1995
Fifty-fifth Supplemental Indenture  . . . . . . . . . . . . . . . . .     March 1, 1996
</TABLE>

which supplemental indentures were or are to be recorded or filed as required
in the State of Texas; and

        WHEREAS, by the Original Indenture, the Company covenanted that it
would execute and deliver such supplemental indenture or indentures and such
further instruments and do such further acts as may be necessary or proper to
carry out more effectually the purposes of the Mortgage and to make subject to
the Lien of the Mortgage any property thereafter acquired and intended to be
subject to the Lien thereof; and

        WHEREAS, in addition to the property described in the Original
Indenture, the Company has acquired certain other property, rights and
interests in property; and
<PAGE>   4
                                       3



        WHEREAS, the Company has heretofore issued as of August 31, 1996, in
accordance with the provisions of the Original Indenture, as heretofore
supplemented, the following series of First Mortgage and Collateral Trust Bonds
and First Mortgage Bonds:

<TABLE>
<CAPTION>
                                                               Principal          Principal
                                                                 Amount             Amount
                 Series                                          Issued          Outstanding
                 ------                                     ---------------      -----------
<S>                                                           <C>               <C>
12% Series due March 1, 1985  . . . . . . . . . . . . . .     $   1,000,000     $     None
13 5/8% Series due April 1, 2014  . . . . . . . . . . . .       100,000,000           None
13 1/2% Series due September 1, 2014  . . . . . . . . . .       150,000,000           None
12 7/8% Series due April 1, 2015  . . . . . . . . . . . .       150,000,000           None
12% Series due August 1, 2015 . . . . . . . . . . . . . .       100,000,000           None
12% Series due September 1, 2015  . . . . . . . . . . . .        75,000,000           None
11 1/8% Series due December 1, 2015 . . . . . . . . . . .       150,000,000           None
9 3/8% Series due March 1, 2016 . . . . . . . . . . . . .       200,000,000           None
9 3/4% Series due May 1, 2016 . . . . . . . . . . . . . .       200,000,000           None
7 3/4% Pollution Control Series C . . . . . . . . . . . .        70,000,000           None
8 1/4% Pollution Control Series D . . . . . . . . . . . .       200,000,000        111,215,000
9 1/2% Series due December 1, 2016  . . . . . . . . . . .       300,000,000           None
9 1/4% Series due February 1, 2017  . . . . . . . . . . .       250,000,000           None
7 7/8% Pollution Control Series E . . . . . . . . . . . .       100,000,000         81,305,000
10 1/2% Series due April 1, 2017  . . . . . . . . . . . .       250,000,000           None
9 1/2% Series due July 1, 1997  . . . . . . . . . . . . .       150,000,000           None
10 1/2% Series due July 1, 2017 . . . . . . . . . . . . .       150,000,000           None
9% Pollution Control Series F   . . . . . . . . . . . . .        55,000,000         51,525,000
9% Pollution Control Series G   . . . . . . . . . . . . .        12,000,000         12,000,000
9 7/8% Pollution Control Series H   . . . . . . . . . . .       112,000,000         28,765,000
9 1/4% Pollution Control Series I   . . . . . . . . . . .       100,000,000         54,005,000
10 3/8% Series due May 1, 1998  . . . . . . . . . . . . .       150,000,000           None
11 3/8% Series due May 1, 2018  . . . . . . . . . . . . .       150,000,000           None
Secured Medium-Term Notes, Series A . . . . . . . . . . .       300,000,000         30,000,000
10.44% Series due November 1, 2008  . . . . . . . . . . .       150,000,000        100,000,000
8 1/4% Pollution Control Series J   . . . . . . . . . . .       100,000,000        100,000,000
9 1/2% Series due August 1, 1999  . . . . . . . . . . . .       200,000,000        200,000,000
10% Series due August 1, 2019 . . . . . . . . . . . . . .       100,000,000           None
9 7/8% Series due November 1, 2019  . . . . . . . . . . .       150,000,000           None
Secured Medium-Term Notes, Series B . . . . . . . . . . .       150,000,000        120,000,000
8 1/8% Pollution Control Series K   . . . . . . . . . . .        50,000,000         50,000,000
8 1/8% Pollution Control Series L   . . . . . . . . . . .        40,000,000         40,000,000
10 5/8% Series due September 1, 2020  . . . . . . . . . .       250,000,000           None
Secured Medium-Term Notes, Series C . . . . . . . . . . .       150,000,000         36,000,000
8 1/4% Pollution Control Series due October 1, 2020 . . .        11,000,000         11,000,000
7 7/8% Pollution Control Series due March 1, 2021 . . . .       100,000,000        100,000,000
9 3/4% Series due May 1, 2021 . . . . . . . . . . . . . .       300,000,000        280,855,000
0% Pollution Control Series M due June 1, 2021  . . . . .        86,250,000           None
0% Pollution Control Series N due June 1, 2021  . . . . .        57,500,000           None
0% Pollution Control Series O due June 1, 2021  . . . . .        57,500,000           None
0% Pollution Control Series P due June 1, 2021  . . . . .       115,000,000         75,831,000
8 1/8% Series due February 1, 2002  . . . . . . . . . . .       150,000,000        150,000,000
8 7/8% Series due February 1, 2022  . . . . . . . . . . .       175,000,000        175,000,000
</TABLE>
<PAGE>   5
                                       4


<TABLE>
<CAPTION>
                                                               Principal          Principal
                                                                 Amount             Amount
                 Series                                          Issued          Outstanding
                 ------                                     ---------------      -----------
<S>                                                           <C>                 <C>
8 1/4% Series due April 1, 2004 . . . . . . . . . . . . .      $100,000,000       $100,000,000
9% Series due April 1, 2022 . . . . . . . . . . . . . . .       100,000,000        100,000,000
6 3/4% Pollution Control Series due April 1, 2022 . . . .        50,000,000         50,000,000
7 1/8% Series due June 1, 1997  . . . . . . . . . . . . .       150,000,000        150,000,000
8% Series due June 1, 2002  . . . . . . . . . . . . . . .       147,000,000        147,000,000
6 5/8% Pollution Control Series due June 1, 2022  . . . .        33,000,000         33,000,000
6 3/8% Series due August 1, 1997  . . . . . . . . . . . .       175,000,000        175,000,000
7 3/8% Series due August 1, 2001  . . . . . . . . . . . .       150,000,000        150,000,000
8 1/2% Series due August 1, 2024  . . . . . . . . . . . .       175,000,000        163,000,000
6.70% Pollution Control Series due October 1, 2022  . . .        16,935,000         16,935,000
6.55% Pollution Control Series due October 1, 2022  . . .        40,000,000         40,000,000
7 3/8% Series due November 1, 1999  . . . . . . . . . . .       100,000,000        100,000,000
8 3/4% Series due November 1, 2023  . . . . . . . . . . .       200,000,000        195,550,000
6 1/2% Pollution Control Series due December 1, 2027  . .        46,660,000         46,660,000
6 3/4% Series due March 1, 2003 . . . . . . . . . . . . .       200,000,000        200,000,000
7 7/8% Series due March 1, 2023 . . . . . . . . . . . . .       300,000,000        300,000,000
6.05% Pollution Control Series due April 1, 2025  . . . .        90,000,000         90,000,000
6.10% Pollution Control Series due April 1, 2028  . . . .        50,000,000         50,000,000
5 7/8% Series due April 1, 1998 . . . . . . . . . . . . .       175,000,000        175,000,000
6 3/4% Series due April 1, 2003 . . . . . . . . . . . . .       100,000,000        100,000,000
7 7/8% Series due April 1, 2024 . . . . . . . . . . . . .       225,000,000        225,000,000
0% Pollution Control Series due June 1, 2023  . . . . . .       115,000,000        115,000,000
5 3/4% Series due July 1, 1998  . . . . . . . . . . . . .       150,000,000        150,000,000
6 3/4% Series due July 1, 2005  . . . . . . . . . . . . .       100,000,000        100,000,000
7 5/8% Series due July 1, 2025  . . . . . . . . . . . . .       250,000,000        250,000,000
5 1/2% Series due October 1, 1998 . . . . . . . . . . . .       125,000,000        125,000,000
6 1/4% Series due October 1, 2004 . . . . . . . . . . . .       125,000,000        125,000,000
7 3/8% Series due October 1, 2025 . . . . . . . . . . . .       300,000,000        253,000,000
5 1/2% Pollution Control Series due May 1, 2022 . . . . .        50,000,000         50,000,000
5.55% Pollution Control Series due May 1, 2022  . . . . .        75,000,000         75,000,000
5.85% Pollution Control Series due May 1, 2022  . . . . .        33,465,000         33,465,000
Floating Rate Series due May 1, 1999  . . . . . . . . . .       300,000,000        300,000,000
Pollution Control Series Q due May 1, 2029  . . . . . . .        45,045,500         45,045,500
Pollution Control Series R due May 1, 2029  . . . . . . .        45,045,500         45,045,500
0% Series due 1994  . . . . . . . . . . . . . . . . . . .     1,013,831,000            None
Pollution Control Series S due April 1, 2030  . . . . . .        58,270,500         58,270,500
Pollution Control Series T due April 1, 2030  . . . . . .        18,400,000         18,400,000
Pollution Control Series U  . . . . . . . . . . . . . . .       136,108,250        136,108,250
Pollution Control Series V  . . . . . . . . . . . . . . .       136,108,250        136,108,250
Pollution Control Series W  . . . . . . . . . . . . . . .        13,857,500         13,857,500
Pollution Control Series X  . . . . . . . . . . . . . . .        21,246,250         21,246,250
Secured Medium-Term Notes, Series D . . . . . . . . . . .       201,150,000        201,150,000
Pollution Control Series Y  . . . . . . . . . . . . . . .        28,819,000         28,819,000
Pollution Control Series Z  . . . . . . . . . . . . . . .        66,642,500         66,642,500
Pollution Control Series AA . . . . . . . . . . . . . . .        28,750,000         28,750,000
Pollution Control Series AB . . . . . . . . . . . . . . .        28,750,000         28,750,000
</TABLE>
<PAGE>   6
                                       5



which bonds are also hereinafter sometimes called bonds of the First through
Eighty-ninth Series, respectively; and

         WHEREAS, Section 2.01 of the Original Indenture provides that the form
of each series of bonds (other than the First Series) issued thereunder and of
the coupons to be attached to coupon bonds of such series shall be established
by Resolution of the Board of Directors of the Company, and that the form of
such series, as established by said Board of Directors, shall specify the
descriptive title of the bonds and various other terms thereof, and may also
have such omissions or modifications or contain such provisions not prohibited
by the provisions of the Mortgage as the Board of Directors may, in its
discretion, cause to be inserted therein expressing or referring to the terms
and conditions upon which such bonds are to  be  issued  and/or  secured  under
the  Mortgage;  and

         WHEREAS, Section 22.04 of the Original Indenture provides, among other
things, that any power, privilege or right expressly or impliedly reserved to
or in any way conferred upon the Company by any provision of the Mortgage,
whether such power, privilege or right is in any way restricted or is
unrestricted, may be in whole or in part waived or surrendered or subjected to
any restriction if at the time unrestricted, or to additional restriction if
already restricted, and the Company may enter into any further covenants,
limitations, restrictions or provisions for the benefit of any one or more
series of bonds issued thereunder, or the Company may cure any ambiguity
contained therein, or in any supplemental indenture, or may establish the terms
and provisions of any series of bonds other than the First Series, by an
instrument in writing executed and acknowledged by the Company in such manner
as would be necessary to entitle a conveyance of real estate to be recorded in
all of the states in which any property at the time subject to the Lien of the
Mortgage shall be situated; and

         WHEREAS, the Company now desires to create two new series of bonds and
to add to its covenants and agreements contained in the Mortgage certain other
covenants and agreements to be observed by it and to alter and amend in certain
respects the covenants and provisions contained in the Mortgage; and

         WHEREAS, the execution and delivery by the Company of this Fifty-sixth
Supplemental Indenture, and the terms of the bonds of the Ninetieth and
Ninety-first Series, hereinafter referred to, have been duly authorized by the
Board of Directors of the Company by appropriate resolutions of said Board of
Directors;

         NOW, THEREFORE, THIS INDENTURE WITNESSETH:  That the Company, in
consideration of the premises and of Ten Dollars to it duly paid by the Trustee
at or before the ensealing and delivery of these presents, the receipt whereof
is hereby acknowledged, and in order to secure the payment of both the
principal of and interest and premium, if any, on the bonds from time to time
issued under the Mortgage, according to their tenor and effect and the
performance of all the provisions of the Mortgage (including any instruments
supplemental thereto and any modification made as in the Mortgage provided) and
of said bonds, hath granted, bargained, sold, released, conveyed, assigned,
transferred, mortgaged, hypothecated, affected, pledged, set over and confirmed
and
<PAGE>   7
                                       6


granted a security interest in and by these presents doth grant, bargain, sell,
release, convey, assign, transfer, mortgage, hypothecate, affect, pledge, set
over and confirm and grant a security interest in (subject, however, to
Excepted Encumbrances as defined in Section 1.06 of the Original Indenture)
unto The Bank of New York, Trustee under the Mortgage, and to its successor or
successors in said trust, and to said Trustee and its successors and assigns
forever, all properties of the Company, real, personal and mixed, of the kind
or nature specifically mentioned in the Original Indenture, as heretofore
supplemented, or of any other kind or nature acquired by the Company on or
after the date of the execution and delivery of the Original Indenture (except
any herein or in the Original Indenture expressly excepted), now owned or,
subject to the provisions of Section 18.03 of the Original Indenture, hereafter
acquired by the Company (by purchase, consolidation, merger, donation,
construction, erection or in any other way) and wheresoever situated, including
(without in anywise limiting or impairing by the enumeration of the same, the
scope and intent of the foregoing or of any general description contained in
this Fifty-sixth Supplemental Indenture) all real estate, lands, easements,
servitudes, licenses, permits, franchises, privileges, rights of way and other
rights in or relating to real estate or the occupancy of the same; all power
sites, flowage rights, water rights, water locations, water appropriations,
ditches, flumes, reservoirs, reservoir sites, canals, raceways, waterways,
dams, dam sites, aqueducts, and all other rights or means for appropriating,
conveying, storing and supplying water; all rights of way and roads; all plants
for the generation of electricity by steam, water and/or other power; all power
houses, gas plants, street lighting systems, standards and other equipment
incidental thereto; all telephone, radio and television systems, air-
conditioning systems and equipment incidental thereto, water wheels, water
works, water systems, steam heat and hot water plants, substations, lines,
service and supply systems, bridges, culverts, tracks, ice or refrigeration
plants and equipment, offices, buildings and other structures and the equipment
thereof; all machinery, engines, boilers, dynamos, turbines, electric, gas and
other machines, prime movers, regulators, meters, transformers, generators
(including, but not limited to, engine driven generators and turbo-generator
units), motors, electrical, gas and mechanical appliances, conduits, cables,
water, steam heat, gas or other pipes, gas mains and pipes, service pipes,
fittings, valves and connections, pole and transmission lines, towers, overhead
conductors and devices, underground conduits, underground conductors and
devices, wires, cables, tools, implements, apparatus, storage battery
equipment, and all other fixtures and personalty; all municipal and other
franchises, consents or permits; all lines for the transmission and
distribution of electric current, gas, steam heat or water for any purpose
including towers, poles, wires, cables, pipes, conduits, ducts and all
apparatus for use in connection therewith and (except as herein or in the
Original Indenture expressly excepted) all the right, title and interest of the
Company in and to all other property of any kind or nature appertaining to
and/or used and/or occupied and/or enjoyed in connection with any property
hereinbefore or in the Original Indenture described.

         TOGETHER WITH all and singular the tenements, hereditaments,
prescriptions, servitudes and appurtenances belonging or in anywise
appertaining to the aforesaid property or any part thereof, with the reversion
and reversions, remainder and remainders and (subject to the provisions of
Section 13.01 of the Original Indenture) the tolls, rents,
<PAGE>   8
                                       7


revenues, issues, earnings, income, product and profits thereof, and all the
estate, right, title and interest and claim whatsoever, at law as well as in
equity, which the Company now has or may hereafter acquire in and to the
aforesaid property and franchises and every part and parcel thereof.

         IT IS HEREBY AGREED by the Company that, subject to the provisions of
Section 18.03 of the Original Indenture, all the property, rights and
franchises acquired by the Company (by purchase, consolidation, merger,
donation, construction, erection or in any other way) after the date hereof,
except any herein or in the Original Indenture expressly excepted, shall be and
are as fully granted and conveyed hereby and as fully embraced within the Lien
of the Original Indenture and the Lien hereof as if such property, rights and
franchises were now owned by the Company and were specifically described herein
and conveyed hereby.

         PROVIDED that the following are not and are not intended to be now or
hereafter granted, bargained, sold, released, conveyed, assigned, transferred,
mortgaged, hypothecated, affected, pledged, set over or confirmed hereunder,
nor is a security interest therein hereby or by the Original Indenture, as
heretofore supplemented, granted or intended to be granted, and the same are
hereby expressly excepted from the Lien and operation of the Original
Indenture, as heretofore supplemented, and from the Lien and operation of this
Fifty-sixth Supplemental Indenture, viz.: (1) cash, shares of stock, bonds,
notes and other obligations and other securities not hereinbefore or hereafter
specifically pledged, paid, deposited, delivered or held under the Mortgage or
covenanted so to be; (2) merchandise, equipment, apparatus, materials or
supplies held for the purpose of sale or other disposition in the usual course
of business or for the purpose of repairing or replacing (in whole or in part)
any rolling stock, buses, motor coaches, automobiles or other vehicles or
aircraft or boats, ships, or other vessels and any fuel, oil and similar
materials and supplies consumable in the operation of any of the properties of
the Company; rolling stock, buses, motor coaches, automobiles and other
vehicles and all aircraft; boats, ships and other vessels; all timber,
minerals, mineral rights and royalties; (3) bills, notes and other instruments
and accounts receivable, judgments, demands, general intangibles and choses in
action, and all contracts, leases and operating agreements not specifically
pledged hereunder or under the Mortgage or covenanted so to be; (4) the last
day of the term of any lease or leasehold which may hereafter become subject to
the Lien of the Mortgage; (5) electric energy, gas, water, steam, ice, and
other materials or products generated, manufactured, produced, or purchased by
the Company for sale, distribution or use in the ordinary course of its
business; (6) any natural gas wells or natural gas leases or natural gas
transportation lines or other works or property used primarily and principally
in the production of natural gas or its transportation, primarily for the
purpose of sale to natural gas customers or to a natural gas distribution or
pipeline company, up to the point of connection with any distribution system;
and (7) the Company's franchise to be a corporation; provided, however, that
the property and rights expressly excepted from the Lien and operation of the
Original Indenture and this Fifty-sixth Supplemental Indenture in the above
subdivisions (2) and (3) shall (to the extent permitted by law) cease to be so
excepted in the event and as of the date that the Trustee or a receiver or
trustee shall enter upon and take possession of the Mortgaged and Pledged
<PAGE>   9
                                       8


Property in the manner provided in Article XV of the Original Indenture by
reason of the occurrence of a Default.

         TO HAVE AND TO HOLD all such properties, real, personal and mixed,
granted, bargained, sold, released, conveyed, assigned, transferred, mortgaged,
hypothecated, affected, pledged, set over or confirmed or in which a security
interest has been granted by the Company as aforesaid, or intended so to be
(subject, however, to Excepted Encumbrances as defined in Section 1.06 of the
Original Indenture), unto The Bank of New York, Trustee, and its successors and
assigns forever.

         IN TRUST NEVERTHELESS, for the same purposes and upon the same terms,
trusts and conditions and subject to and with the same provisos and covenants
as are set forth in the Original Indenture, as heretofore supplemented, this
Fifty- sixth Supplemental Indenture being supplemental to the Original
Indenture.

         AND IT IS HEREBY COVENANTED by the Company that all the terms,
conditions, provisos, covenants and provisions contained in the Original
Indenture, as heretofore supplemented, shall affect and apply to the property
hereinbefore described and conveyed and to the estate, rights, obligations and
duties of the Company and the Trustee and the beneficiaries of the trust with
respect to said property, and to the Trustee and its successors as Trustee of
said property, in the same manner and with the same effect as if said property
had been owned by the Company at the time of the execution of the Original
Indenture, and had been specifically and at length described in and conveyed to
said Trustee by the Original Indenture as a part of the property therein stated
to be conveyed.

         The Company further covenants and agrees to and with the Trustee and
its successors in said trust under the Mortgage, as follows:


                                   ARTICLE I

                           NINETIETH SERIES OF BONDS

         SECTION 1.  There shall be a series of bonds designated "Pollution
Control Series AC" (herein sometimes referred to as the "Ninetieth Series"),
each of which shall also bear the descriptive title "First Mortgage Bond", and
the form thereof, which shall be established by Resolution of the Board of
Directors of the Company, shall contain suitable provisions with respect to the
matters hereinafter in this Section specified.  Bonds of the Ninetieth Series
shall mature on June 1, 2030, shall not bear interest and shall be issued as
fully registered bonds in denominations of One Hundred Twenty-five Dollars and,
at the option of the Company, in any multiple or multiples thereof (the
exercise of such option to be evidenced by the execution and delivery thereof);
the principal of each said bond to be payable at the office or agency of the
Company in the Borough of Manhattan, The City of New York, New York, or at the
office or agency of the Company in the City of Dallas, Texas, as the holder of
any said bond may elect, in such coin or currency of the United States of
America as at the time of payment is legal tender for public and private
<PAGE>   10
                                       9


debts.  Bonds of the Ninetieth Series shall be dated as in Section 2.03 of the
Original Indenture provided.

         (I)  The bonds of the Ninetieth Series shall be initially issued in
the aggregate principal amount of $70,397,250 to, and registered in the name
of, the trustee under the Trust Indenture, dated as of September 1, 1996
(hereinafter sometimes called the "1996B and 1996C Brazos Bond Indenture"), of
the Brazos River Authority (hereinafter sometimes called the "Brazos
Authority"), under which its Collateralized Pollution Control Revenue Refunding
Bonds (Texas Utilities Electric Company Project) Series 1996B (hereinafter
sometimes called the "Series 1996B Brazos Revenue Bonds") are to be issued, in
order to provide the benefit of a lien to secure the obligation of the Company
to make the Installment Payments and Purchase Price payments pursuant to, and
as such terms are defined in, the Installment Sale and Bond Amortization
Agreement, dated as of September 1, 1996 (hereinafter sometimes called the
"1996B Brazos Agreement"), between the Brazos Authority and the Company.

         The Company shall receive a credit against its obligation to make any
payment of the principal of the bonds of the Ninetieth Series, whether at
maturity, upon redemption or otherwise, in an amount equal to 115% of the sum
of (a) the amount, if any, on deposit in the Debt Service Fund maintained under
the 1996B and 1996C Brazos Bond Indenture which reduces the corresponding
Installment Payment and (b) the amount, if any, paid by the Company pursuant to
Section 5.04 of the 1996B Brazos Agreement in respect of the corresponding
Installment Payment.

         The Trustee may conclusively presume that the obligation of the
Company to pay the principal of the bonds of the Ninetieth Series as the same
shall become due and payable shall have been fully satisfied and discharged
unless and until it shall have received a written notice from the trustee under
the 1996B Brazos Bond Indenture, signed by its President, a Vice President, an
Assistant Vice President or a Trust Officer, stating that the corresponding
Installment Payment or Purchase Price payment has become due and payable and
has not been fully paid and specifying the amount of funds required to make
such payment.

         (II)  In the event that any Series 1996B Brazos Revenue Bonds
outstanding under the 1996B and 1996C Brazos Bond Indenture shall become
immediately due and payable pursuant to Section 6.02 of the 1996B and 1996C
Brazos Bond Indenture, upon the occurrence of an Event of Default under Section
6.01(a) of the 1996B and 1996C Brazos Bond Indenture, all bonds of the
Ninetieth Series, then Outstanding, shall be redeemed by the Company, on the
date such Series 1996B Brazos Revenue Bonds shall have become immediately due
and payable, at the principal amount thereof.

         The Trustee may conclusively presume that no redemption of bonds of
the Ninetieth Series is required pursuant to the first paragraph of this
subsection (II) unless and until it shall have received a written notice from
the trustee under the 1996B and 1996C Brazos Bond Indenture, signed by its
President, a Vice President, an Assistant Vice President or a Trust Officer,
stating that Series 1996B Brazos Revenue Bonds have become
<PAGE>   11
                                       10


immediately due and payable pursuant to Section 6.02 of the 1996B and 1996C
Brazos Bond Indenture, upon the occurrence of an Event of Default under Section
6.01(a) of the 1996B and 1996C Brazos Bond Indenture and specifying the
principal amount thereof.  Said notice shall also contain a waiver of notice of
such redemption by the trustee under the 1996B and 1996C Brazos Bond Indenture,
as the holder of all bonds of the Ninetieth Series then Outstanding.

         (III)  The Company hereby waives its right to have any notice of
redemption pursuant to subsection (II) of this Section 1 state that such notice
is subject to the receipt of the redemption moneys by the Trustee on or before
the date fixed for redemption.  Notwithstanding the provisions of Section 12.02
of the Mortgage, any such notice under such subsection shall not be
conditional.

         (IV)  At the option of the registered owner, any bonds of the
Ninetieth Series, upon surrender thereof for cancellation at the office or
agency of the Company in the Borough of Manhattan, The City of New York, New
York, shall be exchangeable for a like aggregate principal amount of bonds of
the same series of other authorized denominations.

         Bonds of the Ninetieth Series shall not be transferrable except to any
successor trustee under the 1996B and 1996C Brazos Bond Indenture, any such
transfer to be made at the office or agency of the Company in the Borough of
Manhattan, The City of New York, New York.

         The Company hereby waives any right to make a charge for any exchange
or transfer of bonds of the Ninetieth Series.



                                   ARTICLE II

                          NINETY-FIRST SERIES OF BONDS

         SECTION 2.  There shall be a series of bonds designated "Pollution
Control Series AD" (herein sometimes referred to as the "Ninety-first Series"),
each of which shall also bear the descriptive title "First Mortgage Bond", and
the form thereof, which shall be established by Resolution of the Board of
Directors of the Company, shall contain suitable provisions with respect to the
matters hereinafter in this Section specified.  Bonds of the Ninety-first
Series shall mature on June 1, 2030, shall not bear interest and shall be
issued as fully registered bonds in denominations of Five Hundred Dollars and,
at the option of the Company, in any multiple or multiples thereof (the
exercise of such option to be evidenced by the execution and delivery thereof);
the principal of each said bond to be payable at the office or agency of the
Company in the Borough of Manhattan, The City of New York, New York, or at the
office or agency of the Company in the City of Dallas, Texas, as the holder of
any said bond may elect, in such coin or currency of the United States of
America as at the time of payment is legal tender for public and private debts.
<PAGE>   12
                                       11


Bonds of the Ninety-first Series shall be dated as in Section 2.03 of the
Original Indenture provided.

         (I)  The bonds of the Ninety-first Series shall be initially issued in
the aggregate principal amount of $57,500,000 to, and registered in the name
of, the trustee under the 1996B and 1996C Brazos Bond Indenture, under which
the Brazos Authority's Collateralized Pollution Control Revenue Refunding Bonds
(Texas Utilities Electric Company Project) Series 1996C (hereinafter sometimes
called the "Series 1996C Brazos Revenue Bonds") are to be issued, in order to
provide the benefit of a lien to secure the obligation of the Company to make
the Installment Payments and Purchase Price payments pursuant to, and as such
terms are defined in, the Installment Sale and Bond Amortization Agreement,
dated as of September 1, 1996 (hereinafter sometimes called the "1996C Brazos
Agreement"), between the Brazos Authority and the Company.

         The Company shall receive a credit against its obligation to make any
payment of the principal of the bonds of the Ninety-first Series, whether at
maturity, upon redemption or otherwise, in an amount equal to 115% of the sum
of (a) the amount, if any, on deposit in the Debt Service Fund maintained under
the 1996B and 1996C Brazos Bond Indenture which reduces the corresponding
Installment Payment and (b) the amount, if any, paid by the Company pursuant to
Section 5.04 of the 1996C Brazos Agreement in respect of the corresponding
Installment Payment.

         The Trustee may conclusively presume that the obligation of the
Company to pay the principal of the bonds of the Ninety-first Series as the
same shall become due and payable shall have been fully satisfied and
discharged unless and until it shall have received a written notice from the
trustee under the 1996B and 1996C Brazos Bond Indenture, signed by its
President, a Vice President, an Assistant Vice President or a Trust Officer,
stating that the corresponding Installment Payment or Purchase Price payment
has become due and payable and has not been fully paid and specifying the
amount of funds required to make such payment.

         (II)  In the event that any Series 1996C Brazos Revenue Bonds
outstanding under the 1996B and 1996C Brazos Bond Indenture shall become
immediately due and payable pursuant to Section 6.02 of the 1996B and 1996C
Brazos Bond Indenture, upon the occurrence of an Event of Default under Section
6.01(a) of the 1996B and 1996C Brazos Bond Indenture, all bonds of the
Ninety-first Series, then Outstanding, shall be redeemed by the Company, on the
date such Series 1996C Brazos Revenue Bonds shall have become immediately due
and payable, at the principal amount thereof.

         The Trustee may conclusively presume that no redemption of bonds of
the Ninety-first Series is required pursuant to the first paragraph of this
subsection (II) unless and until it shall have received a written notice from
the trustee under the 1996B and 1996C Brazos Bond Indenture, signed by its
President, a Vice President, an Assistant Vice President or a Trust Officer,
stating that Series 1996C Brazos Revenue Bonds have become immediately due and
payable pursuant to Section 6.02 of the 1996B and 1996C Brazos Bond Indenture,
upon the occurrence of an Event of Default under Section 6.01(a) of the
<PAGE>   13
                                       12


1996B and 1996C Brazos Bond Indenture and specifying the principal amount
thereof.  Said notice shall also contain a waiver of notice of such redemption
by the trustee under the 1996B and 1996C Brazos Bond Indenture, as the holder
of all bonds of the Ninety-first Series then Outstanding.

         (III)  The Company hereby waives its right to have any notice of
redemption pursuant to subsection (II) of this Section 2 state that such notice
is subject to the receipt of the redemption moneys by the Trustee on or before
the date fixed for redemption.  Notwithstanding the provisions of Section 12.02
of the Mortgage, any such notice under such subsection shall not be
conditional.

         (IV)  At the option of the registered owner, any bonds of the
Ninety-first Series, upon surrender thereof for cancellation at the office or
agency of the Company in the Borough of Manhattan, The City of New York, New
York, shall be exchangeable for a like aggregate principal amount of bonds of
the same series of other authorized denominations.

         Bonds of the Ninety-first Series shall not be transferrable except to
any successor trustee under the 1996B and 1996C Brazos Bond Indenture, any such
transfer to be made at the office or agency of the Company in the Borough of
Manhattan, The City of New York, New York.

         The Company hereby waives any right to make a charge for any exchange
or transfer of bonds of the Ninety-first Series.




                                  ARTICLE III

                            MISCELLANEOUS PROVISIONS

         SECTION 3.  Subject to the amendments provided for in this Fifty-sixth
Supplemental Indenture, the terms defined in the Original Indenture, as
heretofore supplemented, shall for all purposes of this Fifty-sixth
Supplemental Indenture have the meanings specified in the Original Indenture,
as heretofore supplemented.

         SECTION 4.  The Trustee hereby accepts the trusts herein declared,
provided, created or supplemented and agrees to perform the same upon the terms
and conditions herein and in the Original Indenture, as heretofore
supplemented, set forth and upon the following terms and conditions:

         The Trustee shall not be responsible in any manner whatsoever for or
in respect of the validity or sufficiency of this Fifty-sixth Supplemental
Indenture or for or in respect of the recitals contained herein, all of which
recitals are made by the Company solely.  In general, each and every term and
condition contained in Article XIX of the Original
<PAGE>   14
                                       13


Indenture shall apply to and form part of this Fifty-sixth Supplemental
Indenture with the same force and effect as if the same were herein set forth
in full with such omissions, variations and insertions, if any, as may be
appropriate to make the same conform to the provisions of this Fifty-sixth
Supplemental Indenture.

         SECTION 5.  Whenever in this Fifty-sixth Supplemental Indenture either
of the parties hereto is named or referred to, this shall, subject to the
provisions of Articles XVIII and XIX of the Original Indenture, be deemed to
include the successors and assigns of such party, and all the covenants and
agreements in this Fifty-sixth Supplemental Indenture contained, by or on
behalf of the Company, or by or on behalf of the Trustee, shall, subject as
aforesaid, bind and inure to the respective benefits of the respective
successors and assigns of such parties, whether so expressed or not.

         SECTION 6.  Nothing in this Fifty-sixth Supplemental Indenture
expressed or implied, is intended, or shall be construed to confer upon, or to
give to, any person, firm or corporation, other than the parties hereto and the
holders of the bonds and coupons Outstanding under the Mortgage, any right,
remedy or claim under or by reason of this Fifty- sixth Supplemental Indenture
or any covenant, condition, stipulation, promise or agreement hereof, and all
the covenants, conditions, stipulations, promises and agreements in this
Fifty-sixth Supplemental Indenture contained, by or on behalf of the Company,
shall be for the sole and exclusive benefit of the parties hereto, and of the
holders of the bonds and coupons Outstanding under the Mortgage.

         SECTION 7.  This Fifty-sixth Supplemental Indenture shall be executed
in several counterparts, each of which shall be an original and all of which
shall constitute but one and the same instrument.
<PAGE>   15
                                       14



         IN WITNESS WHEREOF, TEXAS UTILITIES ELECTRIC COMPANY has caused its
corporate name to be hereunto affixed, and this instrument to be signed and
sealed by its Chairman of the Board and Chief Executive, President or one of
its Vice Presidents, and its corporate seal to be attested by its Secretary or
one of its Assistant Secretaries for and in its behalf, and THE BANK OF NEW
YORK has caused its corporate name to be hereunto affixed, and this instrument
to be signed and sealed by one of its Vice Presidents or Assistant Vice
Presidents and its corporate seal to be attested by one of its Assistant Vice
Presidents, Assistant Secretaries or Assistant Treasurers, all as of the day
and year first above written.


                                             TEXAS UTILITIES ELECTRIC COMPANY
                                             
                                             
                                             By      /s/  RON SEIDEL          
                                               --------------------------------
                                                          RON SEIDEL
                                                        Vice President
                                             
                                             
Attest:                                      
                                             
   /s/   GLEN H. HIBBS                                  [CORPORATE SEAL]   
---------------------------------------       
         GLEN H. HIBBS
      Assistant Secretary               
                                             
                                                 

Executed, sealed and delivered by
  TEXAS UTILITIES ELECTRIC COMPANY
  in the presence of:


   /s/ W. E. PATTERSON               
-------------------------------------


   /s/ JUSTUS B. RHODES              
-------------------------------------
<PAGE>   16
                                       15




                                                  THE BANK OF NEW YORK, Trustee


                                                  By     /s/ W. N. GITLIN      
                                                    ---------------------------
                                                             W. N. GITLIN
                                                            Vice President
                                                  
Attest:                                           
                                                  
  /s/ STEPHEN J. GIURLANDO                                 [CORPORATE SEAL]
----------------------------------                                       
      STEPHEN J. GIURLANDO                    
     Assistant Vice President               
                                                  
                                                  
Executed, sealed and delivered by                 
  THE BANK OF NEW YORK                            
  in the presence of:                             
                                                  

    /s/ JOCELYN LYNCH             
----------------------------------


    /s/ MICHELLE RUSSO           
----------------------------------
<PAGE>   17
                                       16


STATE OF TEXAS               )
                             )  SS.:
COUNTY OF DALLAS             )


         Before me, a Notary Public in and for said State, on this day
personally appeared RON SEIDEL, known to me to be the person whose name is
subscribed to the foregoing instrument and known to me to be a Vice President
of TEXAS UTILITIES ELECTRIC COMPANY, a Texas corporation, and acknowledged to
me that said person executed said instrument for the purposes and consideration
therein expressed, and as the act of said corporation.

         Given under my hand and seal of office this 18th day of September,
1996.



          [NOTARIAL SEAL]                       /s/  LENAE B. DAVIS    
                                             -----------------------------------
                                                     LENAE B. DAVIS
                                                Notary Public, State of Texas
                                             My Commission Expires June 23, 2000
<PAGE>   18
                                       17



STATE OF NEW YORK               )
                                )  SS.:
COUNTY OF NEW YORK              )


         Before me, a Notary Public in and for said State, on this day
personally appeared W.N. GITLIN, known to me to be the person whose name is
subscribed to the foregoing instrument and known to me to be a Vice President
of THE BANK OF NEW YORK, a New York corporation, and acknowledged to me that
said person executed said instrument for the purposes and consideration therein
expressed, and as the act of said corporation.

         Given under my hand and seal of office this 16th day of September,
1996.




    [NOTARIAL SEAL]                            /s/ WILLIAM J. CASSELS          
                                         --------------------------------------
                                                   WILLIAM J. CASSELS
                                             Notary Public, State of New York
                                                   No. 01CA5027729
                                               Qualified in Bronx County
                                           Certificate filed in New York County
                                             Commission Expires May 16, 1998
<PAGE>   19
                                       18


                           SUMMARY OF RECORDING DATA

                       Fifty-sixth Supplemental Indenture
                            Filed September 26, 1996
                 Office of the Secretary of the State of Texas,
                 Utility Security Instrument File No. 83-281286