Theorem fnfvelrnd

Description: A function's value belongs to its range. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	fnfvelrnd.1	|- ( ph -> F Fn A )
	fnfvelrnd.2	|- ( ph -> B e. A )
Assertion	fnfvelrnd	|- ( ph -> ( F ` B ) e. ran F )

Proof

Step	Hyp	Ref	Expression
1		fnfvelrnd.1	|- ( ph -> F Fn A )
2		fnfvelrnd.2	|- ( ph -> B e. A )
3		fnfvelrn	|- ( ( F Fn A /\ B e. A ) -> ( F ` B ) e. ran F )
4	1 2 3	syl2anc	|- ( ph -> ( F ` B ) e. ran F )