Metamath Proof Explorer

Theorem eqeq12

Description: Equality relationship among four classes. (Contributed by NM, 3-Aug-1994)

Ref Expression
Assertion eqeq12 
|- ( ( 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 ) )