Theorem fveqeq2d

Description: Equality deduction for function value. (Contributed by BJ, 30-Aug-2022)

	Ref	Expression
Hypothesis	fveqeq2d.1	|- ( ph -> A = B )
Assertion	fveqeq2d	|- ( ph -> ( ( F ` A ) = C <-> ( F ` B ) = C ) )

Proof

Step	Hyp	Ref	Expression
1		fveqeq2d.1	|- ( ph -> A = B )
2	1	fveq2d	|- ( ph -> ( F ` A ) = ( F ` B ) )
3	2	eqeq1d	|- ( ph -> ( ( F ` A ) = C <-> ( F ` B ) = C ) )