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Metamath Proof Explorer

Theorem coex

Description: The composition of two sets is a set. (Contributed by NM, 15-Dec-2003)

Ref Expression
Hypotheses coex.1 ⊢ A ∈ V
coex.2 ⊢ B ∈ V
Assertion coex ⊢ A ∘ B ∈ V

Proof

Step Hyp Ref Expression
1 coex.1 ⊢ A ∈ V
2 coex.2 ⊢ B ∈ V
3 coexg ⊢ A ∈ V ∧ B ∈ V → A ∘ B ∈ V
4 1 2 3 mp2an ⊢ A ∘ B ∈ V