Metamath Proof Explorer

Theorem eqeq12

Description: Equality relationship among four classes. (Contributed by NM, 3-Aug-1994) (Proof shortened by Wolf Lammen, 23-Oct-2024)

Ref Expression
Assertion eqeq12 
|- ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( A = B -> A = B )
2 id 
 |-  ( C = D -> C = D )
3 1 2 eqeqan12d 
 |-  ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )