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Metamath Proof Explorer

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