Theorem bnj1149

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj1149.1	⊢ ( 𝜑 → 𝐴 ∈ V )
	bnj1149.2	⊢ ( 𝜑 → 𝐵 ∈ V )
Assertion	bnj1149	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		bnj1149.1	⊢ ( 𝜑 → 𝐴 ∈ V )
2		bnj1149.2	⊢ ( 𝜑 → 𝐵 ∈ V )
3		unexg	⊢ ( ( 𝐴 ∈ V ∧ 𝐵 ∈ V ) → ( 𝐴 ∪ 𝐵 ) ∈ V )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝐴 ∪ 𝐵 ) ∈ V )