Metamath Proof Explorer

Theorem fveq2d

Description: Equality deduction for function value. (Contributed by NM, 29-May-1999)

Ref Expression
Hypothesis fveq2d.1 
|- ( ph -> A = B )
Assertion fveq2d 
|- ( ph -> ( F ` A ) = ( F ` B ) )

Proof

Step Hyp Ref Expression
1 fveq2d.1 
 |-  ( ph -> A = B )
2 fveq2 
 |-  ( A = B -> ( F ` A ) = ( F ` B ) )
3 1 2 syl 
 |-  ( ph -> ( F ` A ) = ( F ` B ) )