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Metamath Proof Explorer

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	$⊢ A \in V$
	Assertion	rnex	$⊢ ran A \in V$

Proof

Step	Hyp	Ref	Expression
1		dmex.1	$⊢ A \in V$
2		rnexg	$⊢ A \in V \to ran A \in V$
3	1 2	ax-mp	$⊢ ran A \in V$