Theorem cnvex

Description: The converse of a set is a set. Corollary 6.8(1) of TakeutiZaring p. 26. (Contributed by NM, 19-Dec-2003)

	Ref	Expression
Hypothesis	cnvex.1	⊢ 𝐴 ∈ V
Assertion	cnvex	⊢ ◡ 𝐴 ∈ V

Proof

Step	Hyp	Ref	Expression
1		cnvex.1	⊢ 𝐴 ∈ V
2		cnvexg	⊢ ( 𝐴 ∈ V → ◡ 𝐴 ∈ V )
3	1 2	ax-mp	⊢ ◡ 𝐴 ∈ V