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Metamath Proof Explorer

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 )