Theorem fvelimabd

Description: Deduction form of fvelimab . (Contributed by Stanislas Polu, 9-Mar-2020)

	Ref	Expression
Hypotheses	fvelimabd.1	|- ( ph -> F Fn A )
	fvelimabd.2	|- ( ph -> B C_ A )
Assertion	fvelimabd	|- ( ph -> ( C e. ( F " B ) <-> E. x e. B ( F ` x ) = C ) )

Proof

Step	Hyp	Ref	Expression
1		fvelimabd.1	|- ( ph -> F Fn A )
2		fvelimabd.2	|- ( ph -> B C_ A )
3		fvelimab	|- ( ( F Fn A /\ B C_ A ) -> ( C e. ( F " B ) <-> E. x e. B ( F ` x ) = C ) )
4	1 2 3	syl2anc	|- ( ph -> ( C e. ( F " B ) <-> E. x e. B ( F ` x ) = C ) )