Metamath Proof Explorer


Theorem eqeq12OLD

Description: Obsolete version of eqeq12 as of 23-Oct-2024. (Contributed by NM, 3-Aug-1994) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Assertion eqeq12OLD
|- ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )

Proof

Step Hyp Ref Expression
1 eqeq1
 |-  ( A = B -> ( A = C <-> B = C ) )
2 eqeq2
 |-  ( C = D -> ( B = C <-> B = D ) )
3 1 2 sylan9bb
 |-  ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )