Theorem fveq12d

Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008)

	Ref	Expression
Hypotheses	fveq12d.1	|- ( ph -> F = G )
	fveq12d.2	|- ( ph -> A = B )
Assertion	fveq12d	|- ( ph -> ( F ` A ) = ( G ` B ) )

Proof

Step	Hyp	Ref	Expression
1		fveq12d.1	|- ( ph -> F = G )
2		fveq12d.2	|- ( ph -> A = B )
3	1	fveq1d	|- ( ph -> ( F ` A ) = ( G ` A ) )
4	2	fveq2d	|- ( ph -> ( G ` A ) = ( G ` B ) )
5	3 4	eqtrd	|- ( ph -> ( F ` A ) = ( G ` B ) )