<PAGE>

                                                                  Exhibit 10(mm)

                                 FIRST AMENDMENT
                                 ---------------

          FIRST AMENDMENT, dated as of June 7, 2001 (this "Amendment"), to the
                                                           ---------
Revolving Credit Agreement, dated as of July 31, 2000 (such Revolving Credit
Agreement, as amended, supplemented or otherwise modified from time to time, the
"Credit Agreement"), among GGP LIMITED PARTNERSHIP, a Delaware limited
 ----------------
partnership (the "Partnership"), GGPLP L.L.C., a Delaware limited liability
                  -----------
company (together with the Partnership, the "Borrower"), the institutions from
                                             --------
time to time parties to the Credit Agreement as Lenders (the "Lenders"), BANK OF
                                                              -------
AMERICA, N.A., as a Lender and as administrative agent for the Lenders (in such
capacity, the "Administrative Agent"), U.S. BANK NATIONAL ASSOCIATION, as a
               --------------------
Lender and as syndication agent for the Lenders (in such capacity, the
"Syndication Agent"), and DRESDNER BANK, AG, New York and Grand Cayman Branches,
 -----------------
as a Lender and as documentation agent for the Lenders (in such capacity, the
"Documentation Agent" and, together with the Administrative Agent and the
 -------------------
Syndication Agent, the "Co-Arrangers").
                        ------------

                              W I T N E S S E T H:
                              - - - - - - - - - -

          WHEREAS, the Borrower and the Lenders have agreed to amend certain
provisions of the Credit Agreement upon the terms and subject to the conditions
set forth herein;

          NOW, THEREFORE, in consideration of the premises and mutual agreements
contained herein, and for other valuable consideration the receipt of which is
hereby acknowledged, the parties hereto hereby agree as follows:

          1. Definitions. All terms defined in the Credit Agreement shall have
             -----------
such defined meanings when used herein unless otherwise defined herein.

          2. Amendment to Section 10.12(i) (Certain Liens). Section 10.12(i) of
             ---------------------------------------------
the Credit Agreement hereby is deleted and the following is inserted in lieu
thereof:

          10.12 (i)  Certain Liens. Neither the Borrower, GGP, Inc. nor any of
                     -------------
     their respective Affiliates controlled by them, respectively, will encumber
     with any Lien any stock, partnership interest, joint venture interest,
     membership interest, beneficial interest or other equity interest in any
     corporation, partnership, joint venture, limited liability company, trust
     or other entity that (i) owns any of the Property, or (ii) is a direct or
     indirect shareholder, partner, joint venturer, member, beneficiary or other
     type of equity holder in any entity described in clause (i) above;
     provided, however, that the foregoing prohibition shall not apply with
     --------  -------
     respect to any of the encumbrances existing on the date hereof set forth in
     Schedule 10.12 hereto; and provided further; that the prohibition set forth
     --------------             ----------------
     in this subsection (i) shall not apply as to any such corporation,
     partnership, joint venture, limited liability company, trust or other
     entity which owns Property with respect to which (A) the Loan-to-Value
     Ratio as to all Secured Indebtedness for borrowed money related to such
     Property, in the aggregate, after giving effect to such encumbrance, is not
     greater than sixty-five percent (65%) and (B) the Loan-to-Value Ratio as to
     that portion of such Secured Indebtedness which is secured by such a Lien
     encumbering any stock,

<PAGE>

     partnership interest, joint venture interest, membership interest,
     beneficial interest or other equity interest is not greater than fifteen
     percent (15%); and provided further that the prohibition set forth in this
                        -------- -------
     subsection (i) shall not apply as to any such encumbrance granted to secure
     Indebtedness related to any Property or asset of such corporation,
     partnership, joint venture, limited liability company, trust or other
     entity, if such encumbrance secures a construction loan and the
     Loan-to-Value Ratio with respect to all Secured Indebtedness relating to
     the construction in question does not exceed seventy-five percent (75%), or
     would not exceed such Loan-to-Value Ratio, but for the applicability of
     unusually onerous stamp, transfer or recording taxes and fees in connection
     with such encumbrance; and provided further that the prohibition set forth
                                -------- -------
     in this subsection (i) shall not apply as to any such encumbrance of equity
     interests in Minority Holdings in favor of holders(s) of the remaining
     equity interests in such Minority Holdings to secure obligations under the
     applicable Organizational Documents of such Minority Holdings.

          3.  Representations; No Default. On and as of the date hereof, and
              ---------------------------
after giving effect to this Amendment, (i) the Borrower certifies that no
Default or Event of Default has occurred which is continuing, and (ii) the
Borrower confirms, reaffirms and restates that the representations and
warranties set forth in Article VII of the Credit Agreement and in the other
Loan Documents to which it is a party are true and correct in all material
respects, provided that the references to the Credit Agreement therein shall be
          --------
deemed to be references to this Amendment and to the Credit Agreement as amended
by this Amendment.

          4.  Conditions to Effectiveness. This Amendment shall become effective
              ---------------------------
on and as of the date that:

          (a) the Administrative Agent shall have received counterparts of this
     Amendment, duly executed and delivered by a duly authorized officer of the
     Borrower and the Lenders; and

          (b) the Administrative Agent shall have received an executed
     Acknowledgment and Consent, in the form set forth at the end of this
     Amendment, from GGP, Inc.

          5.  Limited Consent and Amendment. Except as expressly amended herein,
              -----------------------------
the Credit Agreement shall continue to be, and shall remain, in full force and
effect. This Amendment shall not be deemed to be a waiver of, or consent to, or
a modification or amendment of, any other term or condition of the Credit
Agreement or any other Loan Document or to prejudice any other right or rights
which the Co-Arrangers or the Lenders may now have or may have in the future
under or in connection with the Credit Agreement or any of the instruments or
agreements referred to therein, as the same may be amended from time to time.

          6.  Counterparts. This Amendment may be executed by one or more of the
              ------------
parties hereto in any number of separate counterparts and all of said
counterparts taken together shall be deemed to constitute one and the same
instrument.

<PAGE>

          7. GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED
             -------------
AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF ILLINOIS.

                     (REMAINDER OF PAGE INTENTIONALLY BLANK)

<PAGE>

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed and delivered by their respective duly authorized officers as of the
date first above written.

                                    GGP LIMITED PARTNERSHIP, as Borrower

                                    By:     GENERAL GROWTH PROPERTIES, INC., its
                                            sole general partner


                                    By: /s/ Bernard Freibaum
                                        ----------------------------------------
                                        Name:  Bernard Freibaum
                                        Title: Executive Vice President


                                    GGPLP L.L.C., as Borrower

                                    By:     GGP LIMITED PARTNERSHIP, its sole
                                            managing member

                                    By:     GENERAL GROWTH PROPERTIES, INC., its
                                            sole general partner


                                    By: /s/ Bernard Freibaum
                                        ----------------------------------------
                                        Name:  Bernard Freibaum
                                        Title: Executive Vice President


                                    BANK OF AMERICA, N.A.,
                                      as Administrative Agent and as a Lender


                                    By: /s/ Ronald B. Phemister
                                        ----------------------------------------
                                        Name:  Ronald B. Phemister
                                        Title: Principal


                                    U.S. BANK NATIONAL ASSOCIATION,
                                      as Syndication Agent and as a Lender


                                    By: /s/ Gregory S. Pearson
                                        ----------------------------------------
                                        Name:  Gregory S. Pearson
                                        Title: Commercial Banking Officer

<PAGE>

                                DRESDNER BANK AG, NEW YORK AND GRAND CAYMAN
                                BRANCHES,
                                 as Documentation Agent and as a Lender


                                By: /s/ Maureen Slentz     /s/ Brian Huddlestun
                                    --------------------------------------------
                                    Name:  Maureen Slentz      Brian Huddlestun
                                    Title: Director            Vice President


                                BAYERISCHE HYPO-UND VEREINSBANK, NEW YORK
                                BRANCH, as a Lender


                                By: /s/ Christine Elcik    /s/ Meggan W. Walsh
                                    --------------------------------------------
                                    Name:  Christine Elcik     Meggan W. Walsh
                                    Title: Associate Director  Managing Director

<PAGE>

                           ACKNOWLEDGMENT AND CONSENT

     The undersigned party to the Guaranty, dated as of July 31, 2000 and as
amended, supplemented or otherwise modified from time to time, made by the
undersigned in favor of Bank of America, N.A., as Administrative Agent, for the
benefit of the Lenders, hereby (a) consents to the transactions contemplated by
the foregoing First Amendment and (b) acknowledges and agrees that the
guarantees contained in the Guaranty are, and shall remain, in full force and
effect after giving effect to such Amendment to the Credit Agreement.

                                             GENERAL GROWTH PROPERTIES, INC.


                                             By: /s/ Bernard Freibaum
                                                 -------------------------------
                                                 Name:  Bernard Freibaum
                                                 Title: Executive Vice President