Theorem dmex

Description: The domain of a set is a set. Corollary 6.8(2) of TakeutiZaring p. 26. (Contributed by NM, 7-Jul-2008)

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

Proof

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