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 ∈ V
	unex.2	⊢ 𝐵 ∈ V
Assertion	unex	⊢ ( 𝐴 ∪ 𝐵 ) ∈ V

Proof

Step	Hyp	Ref	Expression
1		unex.1	⊢ 𝐴 ∈ V
2		unex.2	⊢ 𝐵 ∈ V
3		unexg	⊢ ( ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) → ( 𝐴 ∪ 𝐵 ) ∈ V )
4	1 2 3	mp2an	⊢ ( 𝐴 ∪ 𝐵 ) ∈ V