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	$$⊢\phi \to FFnA$$
	fnexd.2	$$⊢\phi \to A\in V$$
Assertion	fnexd	$$⊢\phi \to F\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		fnexd.1	$$⊢\phi \to FFnA$$
2		fnexd.2	$$⊢\phi \to A\in V$$
3		fnex	$$⊢\left(FFnA\wedge A\in V\right)\to F\in \mathrm{V}$$
4	1 2 3	syl2anc	$$⊢\phi \to F\in \mathrm{V}$$