<PAGE>

                                                                   EXHIBIT 99.06

                     MONTHLY CERTIFICATEHOLDERS' STATEMENT

                     FIRST USA BANK, NATIONAL ASSOCIATION

             -----------------------------------------------------
               FIRST USA CREDIT CARD MASTER TRUST, SERIES 1995-6
             -----------------------------------------------------

                   Monthly Period:                  5/1/00 to
                                                    5/31/00
                   Distribution Date:               6/12/00
                   Transfer Date:                   6/9/00

Under Section 5.02 of the Pooling and Servicing Agreement dated as of September
1, 1992 (the "Pooling and Servicing Agreement") by and between First USA Bank,
National Association, (the "Bank") and The Bank of New York (Delaware), as
trustee (the "Trustee") the Bank, as Servicer, is required to prepare certain
information each month regarding current distributions to Certificateholders and
the performance of the First USA Credit Card Master Trust (the "Trust") during
the previous month. The information which is required to be prepared with
respect to the Distribution Date noted above and with respect to the performance
of the Trust during the month noted above is set forth below. Certain
information is presented on the basis of an original principal amount of $1,000
per Series 1995-6 Certificate (a "Certificate"). Certain other information is
presented based on the aggregate amount for the Trust as a whole. Capitalized
terms used in this Monthly Certificateholders' Statement have their respective
meanings set forth in the Pooling and Servicing Agreement.

A.   Information Regarding the Current Monthly Distribution.
     -------------------------------------------------------

<TABLE>
         <S>                                                                                  <C>
         1.    The total amount of the distribution to
               Certificateholders on the Distribution Date per
               $1,000 original certificate principal amount

                                                           Class A                            $6.07865
                                                           Class B                            $6.22531
                                                           CIA                                $6.79365
                                                                                              --------
                                                               Total (Weighted Avg.)          $6.15757


         2.    The amount of the distribution set forth in
               paragraph 1 above in respect of interest on
               the Certificates, per $1,000 original
               certificate principal amount

                                                           Class A                            $6.07865
                                                           Class B                            $6.22531
                                                           CIA                                $6.79365
                                                                                              --------
                                                               Total (Weighted Avg.)          $6.15757
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT                             Series 1995-6
Page 2

<TABLE>
         <S>                                                                                         <C>
         3.    The amount of the distribution set forth in paragraph 1
               above in respect of principal on the Certificates, per
               $1,000 original certificate principal amount

                                                                     Class A                         $0.00000
                                                                     Class B                         $0.00000
                                                                     CIA                             $0.00000
                                                                                                     --------
                                                                     Total (Weighted Avg.)           $0.00000

B.       Information Regarding the Performance of the Trust.
         ---------------------------------------------------

         1.    Allocation of Principal Receivables.
               ------------------------------------

               The aggregate amount of Allocations of Principal Receivables
               processed during the Monthly Period which were allocated in
               respect of the Certificates

                                                                     Class A                  $175,874,880.02
                                                                     Class B                   $15,900,877.39
                                                                     CIA                       $20,117,403.95
                                                                                              ---------------
                                                                     Total                    $211,893,161.36

         2.    Allocation of Finance Charge Receivables
               ----------------------------------------

               (a1)   The aggregate amount of Allocations of Finance Charge
                      Receivables processed during the Monthly Period which were
                      allocated in respect of the Certificates

                                                                     Class A                   $18,510,243.55
                                                                     Class B                    $1,673,514.20
                                                                     CIA                        $2,117,289.56
                                                                                               --------------
                                                                     Total                     $22,301,047.31

               (b1)   Principal Funding Investment Proceeds (to Class A)                                $0.00
               (b2)   Withdrawals from Reserve Account (to Class A)                                     $0.00
                                                                                               --------------
                      Class A Available Funds                                                  $18,510,243.55


         3.    Principal Receivable / Investor Percentages
               -------------------------------------------

               (a)    The aggregate amount of Principal Receivables in
                      the Trust as of the last day of the Monthly Period                   $36,124,641,027.99
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT                             Series 1995-6
Page 3

<TABLE>
               <S>                                                                       <C>
               (b)    Invested Amount as of the last day of the preceding
                      month (Adjusted Class A Invested Amount
                      during Accumulation Period)
                                                                     Class A             $1,245,000,000.00
                                                                     Class B             $  112,500,000.00
                                                                     CIA                 $  142,500,000.00
                                                                                         -----------------
                                                                     Total               $1,500,000,000.00


               (c)    The Floating Allocation Percentage: The Invested
                      Amount set forth in paragraph 3(b) above as a
                      percentage of the aggregate amount of Principal
                      Receivables as of the Record Date set forth in
                      paragraph 3(a) above
                                                                     Class A                         3.446%
                                                                     Class B                         0.311%
                                                                     CIA                             0.394%
                                                                                                     -----
                                                                     Total                           4.151%

               (d)    During the Amortization Period: The Invested Amount
                      as of ______ (the last day of the Revolving Period)
                                                                     Class A                         $0.00
                                                                     Class B                         $0.00
                                                                     CIA                             $0.00
                                                                                                     -----
                                                                     Total                           $0.00

               (e)    The Fixed/Floating Allocation Percentage: The Invested
                      Amount set forth in paragraph 3(d) above as a
                      percentage of the aggregate amount of Principal
                      Receivables set forth in paragraph 3(a) above
                                                                     Class A                         0.000%
                                                                     Class B                         0.000%
                                                                     CIA                             0.000%
                                                                                                     -----
                                                                     Total                           0.000%
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT                             Series 1995-6
Page 4

<TABLE>
        <S>                                                                             <C>
         4.    Delinquent Balances.
               --------------------

               The aggregate amount of outstanding balances in the Accounts
               which were delinquent as of the end of the day on the last day of
               the Monthly Period

               (a)    35 - 64 days                                                      $  428,403,170.53
               (b)    65 - 94 days                                                      $  277,772,886.82
               (c)    95 - 124 days                                                     $  231,052,772.40
               (d)    125 - 154 days                                                    $  196,167,513.76
               (e)    155 - 184 days                                                    $  164,129,162.83
               (f)    185 or more days                                                  $            0.00
                                                                                        -----------------
                                                                     Total              $1,297,525,506.34

         5.    Monthly Investor Default Amount.
               --------------------------------

               (a)    The aggregate amount of all defaulted Principal
                      Receivables written off as uncollectible during the
                      Monthly Period allocable to the Invested Amount (the
                      aggregate "Investor Default Amount")
                                                                     Class A               $ 8,352,723.58
                                                                     Class B               $   755,171.14
                                                                     CIA                   $   955,424.19
                                                                                           --------------
                                                                     Total                 $10,063,318.91


         6.    Investor Charge-Offs & Reimbursements of Charge-Offs.
               -----------------------------------------------------

               (a)    The aggregate amount of Class A Investor Charge-
                      Offs and the reductions in the Class B Invested
                      Amount and the CIA
                                                                     Class A                        $0.00
                                                                     Class B                        $0.00
                                                                     CIA                            $0.00
                                                                                                   ------
                                                                     Total                          $0.00

               (b)    The amounts set forth in paragraph 6(a) above, per $1,000
                      original certificate principal amount (which will have the
                      effect of reducing, pro rata, the amount of each
                      Certificateholder's investment)
                                                                     Class A                        $0.00
                                                                     Class B                        $0.00
                                                                     CIA                            $0.00
                                                                                                   ------
                                                                     Total                          $0.00
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT                             Series 1995-6
Page 5

<TABLE>
              <S>                                                                    <C>
               (c)    The aggregate amount of Class A Investor Charge-
                      Offs reimbursed and the reimbursement of
                      reductions in the Class B Invested Amount and the
                      CIA

                                                       Class A                                 $0.00
                                                       Class B                                 $0.00
                                                       CIA                                     $0.00
                                                                                               -----
                                                       Total                                   $0.00

               (d)    The amounts set forth in paragraph 6(c) above, per $1,000
                      interest (which will have the effect of increasing, pro
                      rata, the amount of each Certificateholder's investment)
                                                       Class A                                 $0.00
                                                       Class B                                 $0.00
                                                       CIA                                     $0.00
                                                                                               -----
                                                       Total                                   $0.00

         7.    Investor Servicing Fee
               ---------------------
               (a)    The amount of the Investor Monthly Servicing Fee
                      payable by the Trust to the Servicer for the
                      Monthly Period

                                                       Class A                         $1,556,250.00
                                                       Class B                         $  140,625.00
                                                       CIA                             $  178,125.00
                                                                                       -------------
                                                       Total                           $1,875,000.00


         8.    Reallocated Principal Collections
               ---------------------------------
                      The amount of Reallocated CIA
                      and Class B Principal Collections applied in respect of
                      Interest Shortfalls, Investor Default Amounts or Investor
                      Charge-Offs for the prior month.

                                                       Class B                                 $0.00
                                                       CIA                                     $0.00
                                                                                               -----
                                                       Total                                   $0.00

         9.    Collateral Invested Amount
               (a)    The amount of the Collateral Invested Amount as of the
                      close of business on the related Distribution Date after
                      giving effect to withdrawals, deposits and payments to
                      be made in respect of the preceding month                      $142,500,000.00
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT                             Series 1995-6
Page 6

<TABLE>
              <S>                                                                     <C>
               (b)    The Required CIA Invested Amount as of the
                      close of business on the related Distribution Date after
                      giving effect to withdrawals, deposits and payments to
                      be made in respect of the preceding month                         $142,500,000.00

         10.   The Pool Factor
               ---------------
                      The Pool Factor (which represents the ratio of the amount
                      of the Investor Interest on the last day of the Monthly
                      Period, inclusive of any principal payments to be made on
                      the related Distribution Date, to the amount of the
                      Investor Interest as of the Closing Date). The amount of a
                      Certificateholder's pro rata share of the Investor
                      Participation Amount can be determined by multiplying the
                      original denomination of the holder's Certificate by the
                      Pool Factor

                                                                       Class A               1.00000000
                                                                       Class B               1.00000000
                                                                       Total                 1.00000000
         11.   The Portfolio Yield
               -------------------
                  The Portfolio Yield for the related Monthly Period                              9.79%

         12.   The Base Rate
               -------------
                  The Base Rate for the related Monthly Period                                    8.72%



  C      Information Regarding the Principal Funding Acccount
         ----------------------------------------------------

             1.   Accumulation Period

             (a)  Accumulation Period commencement date                                      10/01/2000

             (b)  Accumulation Period Length (months)                                                 1

             (c)  Accumulation Period Factor                                                      20.31

             (d)  Required Accumulation Factor Number                                                 8

             (e)  Controlled Accumulation Amount                                      $1,245,000,000.00

             (f)  Minimum Payment Rate (last 12 months)                                          14.06%
</TABLE>
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MONTHLY CERTIFICATEHOLDERS' STATEMENT                              Series 1995-6
Page 7

<TABLE>
             <S>                                                                 <C>
             2.   Principal Funding Account
                  -------------------------

                  Beginning Balance                                                $0.00
                       Plus:    Principal Collections for related Monthly Period
                                Principal Account                                  $0.00
                       Plus:    Interest on Principal Funding Account Balance for
                                related Monthly Period                             $0.00

                       Less:    Withdrawals to Finance Charge Account              $0.00
                       Less:    Withdrawals to Distribution Account                $0.00
                                                                                 -------
                  Ending Balance                                                   $0.00

             3.   Accumulation Shortfall
                  ----------------------

                           The Controlled Deposit Amount for the previous

                           Monthly Period                                          $0.00

                  Less:    The amount deposited into the Principal Funding
                           Account for the Previous Monthly Period                 $0.00

                           Accumulation Shortfall                                  $0.00

                                                                                 -------
                           Aggregate Accumulation Shortfalls                       $0.00

             4.   Principal Funding Investment Shortfall
                  --------------------------------------

                           Covered Amount                                          $0.00

                  Less:    Principal Funding Investment Proceeds                   $0.00

                                                                                 -------
                           Principal Funding Investment Shortfall                  $0.00
                                                                                 -------

  D.   Information Regarding the Reserve Account
       -----------------------------------------

             1.   Required Reserve Account Analysis
                  ----------------------------------

                  (a)  Required Reserve Account Amount percentage                0.00000%

                  (b)  Required Reserve Account Amount ($)                         $0.00
                       (0.5% of Invested Amount or other amount
                       designated by Transferor)

                  (c)  Required Reserve Account Balance after effect of
                       any transfers on the Related Transfer Date                  $0.00

                  (d)  Reserve Draw Amount transferred to the Finance
                       Charge Account on the Related Transfer Date                 $0.00
</TABLE>
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MONTHLY CERTIFICATEHOLDERS' STATEMENT                              Series 1995-6
Page 8

<TABLE>
            <S>                                                                     <C>
             2.   Reserve Account Investment Proceeds
                  -----------------------------------
                  Reserve Account Investment Proceeds transferred to the
                  Finance Charge Account on the Related Transfer Date               $0.00

             3.   Withdrawals from the Reserve Account
                  ------------------------------------
                  Total Withdrawals from the Reserve Account transferred
                  to the Finance Charge Account on the related Transfer             $0.00
                  Date (1 (d) plus 2 above)

             4.   The Portfolio Adjusted Yield
                  ----------------------------
                  The Portfolio Adjusted Yield for the related Monthly Period       3.34%
</TABLE>
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MONTHLY CERTIFICATEHOLDER'S STATEMENT
Signature Page





                                        First USA Bank, National Association
                                        as Servicer




                                        By:  /s/ Tracie Klein
                                             --------------------
                                             Tracie Klein
                                             First Vice President