Theorem fexd

Description: If the domain of a mapping is a set, the function is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypotheses	fexd.1	$$⊢\phi \to F:A⟶B$$
	fexd.2	$$⊢\phi \to A\in C$$
Assertion	fexd	$$⊢\phi \to F\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		fexd.1	$$⊢\phi \to F:A⟶B$$
2		fexd.2	$$⊢\phi \to A\in C$$
3		fex	$$⊢\left(F:A⟶B\wedge A\in C\right)\to F\in \mathrm{V}$$
4	1 2 3	syl2anc	$$⊢\phi \to F\in \mathrm{V}$$