Theorem fvclex

Description: Existence of the class of values of a set. (Contributed by NM, 9-Nov-1995)

	Ref	Expression
Hypothesis	fvclex.1	$$⊢F\in \mathrm{V}$$
Assertion	fvclex	$$⊢\left\{y|\exists xy=F\left(x\right)\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		fvclex.1	$$⊢F\in \mathrm{V}$$
2	1	rnex	$$⊢\mathrm{ran}F\in \mathrm{V}$$
3		snex	$$⊢\left\{\varnothing \right\}\in \mathrm{V}$$
4	2 3	unex	$$⊢\mathrm{ran}F\cup \left\{\varnothing \right\}\in \mathrm{V}$$
5		fvclss	$$⊢\left\{y|\exists xy=F\left(x\right)\right\}\subseteq \mathrm{ran}F\cup \left\{\varnothing \right\}$$
6	4 5	ssexi	$$⊢\left\{y|\exists xy=F\left(x\right)\right\}\in \mathrm{V}$$