Metamath Proof Explorer

Theorem afveq1

Description: Equality theorem for function value, analogous to fveq1 . (Contributed by Alexander van der Vekens, 22-Jul-2017)

Ref Expression
Assertion afveq1 
|- ( F = G -> ( F ''' A ) = ( G ''' A ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( F = G -> F = G )
2 eqidd 
 |-  ( F = G -> A = A )
3 1 2 afveq12d 
 |-  ( F = G -> ( F ''' A ) = ( G ''' A ) )