Theorem bnj1502

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1502.1	|- ( ph -> Fun F )
	bnj1502.2	|- ( ph -> G C_ F )
	bnj1502.3	|- ( ph -> A e. dom G )
Assertion	bnj1502	|- ( ph -> ( F ` A ) = ( G ` A ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1502.1	|- ( ph -> Fun F )
2		bnj1502.2	|- ( ph -> G C_ F )
3		bnj1502.3	|- ( ph -> A e. dom G )
4		funssfv	|- ( ( Fun F /\ G C_ F /\ A e. dom G ) -> ( F ` A ) = ( G ` A ) )
5	1 2 3 4	syl3anc	|- ( ph -> ( F ` A ) = ( G ` A ) )