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Metamath Proof Explorer

Theorem uniex

Description: The Axiom of Union in class notation. This says that if A is a set i.e. A e. _V (see isset ), then the union of A is also a set. Same as Axiom 3 of TakeutiZaring p. 16. (Contributed by NM, 11-Aug-1993)

		Ref	Expression
	Hypothesis	uniex.1	$⊢ A \in V$
	Assertion	uniex	$⊢ ⋃ A \in V$

Proof

Step	Hyp	Ref	Expression
1		uniex.1	$⊢ A \in V$
2		uniexg	$⊢ A \in V \to ⋃ A \in V$
3	1 2	ax-mp	$⊢ ⋃ A \in V$