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	$$⊢A\in \mathrm{V}$$
Assertion	uniex	$$⊢\bigcup A\in \mathrm{V}$$

Proof

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