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Metamath Proof Explorer

Theorem uniexb

Description: The Axiom of Union and its converse. A class is a set iff its union is a set. (Contributed by NM, 11-Nov-2003)

		Ref	Expression
	Assertion	uniexb	$⊢ A \in V \leftrightarrow ⋃ A \in V$

Step	Hyp	Ref	Expression
1		uniexg	$⊢ A \in V \to ⋃ A \in V$
2		uniexr	$⊢ ⋃ A \in V \to A \in V$
3	1 2	impbii	$⊢ A \in V \leftrightarrow ⋃ A \in V$