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Metamath Proof Explorer

Theorem breq12

Description: Equality theorem for a binary relation. (Contributed by NM, 8-Feb-1996)

Ref Expression
Assertion breq12 
|- ( ( A = B /\ C = D ) -> ( A R C <-> B R D ) )

Proof

Step Hyp Ref Expression
1 breq1 
 |-  ( A = B -> ( A R C <-> B R C ) )
2 breq2 
 |-  ( C = D -> ( B R C <-> B R D ) )
3 1 2 sylan9bb 
 |-  ( ( A = B /\ C = D ) -> ( A R C <-> B R D ) )