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 ∈ V
Assertion	dmex	⊢ dom 𝐴 ∈ V

Proof

Step	Hyp	Ref	Expression
1		dmex.1	⊢ 𝐴 ∈ V
2		dmexg	⊢ ( 𝐴 ∈ V → dom 𝐴 ∈ V )
3	1 2	ax-mp	⊢ dom 𝐴 ∈ V