Metamath Proof Explorer

Theorem oveq12

Description: Equality theorem for operation value. (Contributed by NM, 16-Jul-1995)

Ref Expression
Assertion oveq12 
|- ( ( A = B /\ C = D ) -> ( A F C ) = ( B F D ) )

Proof

Step Hyp Ref Expression
1 oveq1 
 |-  ( A = B -> ( A F C ) = ( B F C ) )
2 oveq2 
 |-  ( C = D -> ( B F C ) = ( B F D ) )
3 1 2 sylan9eq 
 |-  ( ( A = B /\ C = D ) -> ( A F C ) = ( B F D ) )