Theorem unex

Description: The union of two sets is a set. Corollary 5.8 of TakeutiZaring p. 16. (Contributed by NM, 1-Jul-1994)

	Ref	Expression
Hypotheses	unex.1	$$⊢A\in \mathrm{V}$$
	unex.2	$$⊢B\in \mathrm{V}$$
Assertion	unex	$$⊢A\cup B\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		unex.1	$$⊢A\in \mathrm{V}$$
2		unex.2	$$⊢B\in \mathrm{V}$$
3	1 2	unipr	$$⊢\bigcup \left\{A,B\right\}=A\cup B$$
4		prex	$$⊢\left\{A,B\right\}\in \mathrm{V}$$
5	4	uniex	$$⊢\bigcup \left\{A,B\right\}\in \mathrm{V}$$
6	3 5	eqeltrri	$$⊢A\cup B\in \mathrm{V}$$