Metamath Proof Explorer

Theorem oveq2

Description: Equality theorem for operation value. (Contributed by NM, 28-Feb-1995)

Ref Expression
Assertion oveq2 
|- ( A = B -> ( C F A ) = ( C F B ) )

Proof

Step Hyp Ref Expression
1 opeq2 
 |-  ( A = B -> <. C , A >. = <. C , B >. )
2 1 fveq2d 
 |-  ( A = B -> ( F ` <. C , A >. ) = ( F ` <. C , B >. ) )
3 df-ov 
 |-  ( C F A ) = ( F ` <. C , A >. )
4 df-ov 
 |-  ( C F B ) = ( F ` <. C , B >. )
5 2 3 4 3eqtr4g 
 |-  ( A = B -> ( C F A ) = ( C F B ) )