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 ∈ V
Assertion	rnex	⊢ ran 𝐴 ∈ V

Proof

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