Theorem bnj1503

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

	Ref	Expression
Hypotheses	bnj1503.1	|- ( ph -> Fun F )
	bnj1503.2	|- ( ph -> G C_ F )
	bnj1503.3	|- ( ph -> A C_ dom G )
Assertion	bnj1503	|- ( ph -> ( F |` A ) = ( G |` A ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1503.1	|- ( ph -> Fun F )
2		bnj1503.2	|- ( ph -> G C_ F )
3		bnj1503.3	|- ( ph -> A C_ dom G )
4		fun2ssres	|- ( ( Fun F /\ G C_ F /\ A C_ dom G ) -> ( F |` A ) = ( G |` A ) )
5	1 2 3 4	syl3anc	|- ( ph -> ( F |` A ) = ( G |` A ) )