Theorem dmexd

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

	Ref	Expression
Hypothesis	dmexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	dmexd	⊢ ( 𝜑 → dom 𝐴 ∈ V )

Proof

Step	Hyp	Ref	Expression
1		dmexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		dmexg	⊢ ( 𝐴 ∈ 𝑉 → dom 𝐴 ∈ V )
3	1 2	syl	⊢ ( 𝜑 → dom 𝐴 ∈ V )