Theorem dmexd

Description: The domain of a set is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

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

Proof

Step	Hyp	Ref	Expression
1		dmexd.1	$$⊢\phi \to A\in V$$
2		dmexg	$$⊢A\in V\to \mathrm{dom}A\in \mathrm{V}$$
3	1 2	syl	$$⊢\phi \to \mathrm{dom}A\in \mathrm{V}$$