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Metamath Proof Explorer

Theorem imaexg

Description: The image of a set is a set. Theorem 3.17 of Monk1 p. 39. (Contributed by NM, 24-Jul-1995)

		Ref	Expression
	Assertion	imaexg	$⊢ A \in V \to A [B] \in V$

Step	Hyp	Ref	Expression
1		imassrn	$⊢ A [B] \subseteq ran A$
2		rnexg	$⊢ A \in V \to ran A \in V$
3		ssexg	$⊢ (A [B] \subseteq ran A \land ran A \in V) \to A [B] \in V$
4	1 2 3	sylancr	$⊢ A \in V \to A [B] \in V$