Theorem rnex

Description: The range of a set is a set. Corollary 6.8(3) of TakeutiZaring p. 26. Similar to Lemma 3D of Enderton p. 41. (Contributed by NM, 7-Jul-2008)

	Ref	Expression
Hypothesis	dmex.1	$$⊢A\in \mathrm{V}$$
Assertion	rnex	$$⊢\mathrm{ran}A\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		dmex.1	$$⊢A\in \mathrm{V}$$
2		rnexg	$$⊢A\in \mathrm{V}\to \mathrm{ran}A\in \mathrm{V}$$
3	1 2	ax-mp	$$⊢\mathrm{ran}A\in \mathrm{V}$$