Theorem fnexd

Description: If the domain of a function is a set, the function is a set. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	fnexd.1	|- ( ph -> F Fn A )
	fnexd.2	|- ( ph -> A e. V )
Assertion	fnexd	|- ( ph -> F e. _V )

Proof

Step	Hyp	Ref	Expression
1		fnexd.1	|- ( ph -> F Fn A )
2		fnexd.2	|- ( ph -> A e. V )
3		fnex	|- ( ( F Fn A /\ A e. V ) -> F e. _V )
4	1 2 3	syl2anc	|- ( ph -> F e. _V )