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Metamath Proof Explorer

Theorem elrn2

Description: Membership in a range. (Contributed by NM, 10-Jul-1994)

		Ref	Expression
	Hypothesis	elrn.1	$⊢ A \in V$
	Assertion	elrn2	$⊢ A \in ran B \leftrightarrow \exists x ⟨x, A⟩ \in B$

Step	Hyp	Ref	Expression
1		elrn.1	$⊢ A \in V$
2		elrn2g	$⊢ A \in V \to (A \in ran B \leftrightarrow \exists x ⟨x, A⟩ \in B)$
3	1 2	ax-mp	$⊢ A \in ran B \leftrightarrow \exists x ⟨x, A⟩ \in B$