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