Theorem funcnvcnv

Description: The double converse of a function is a function. (Contributed by NM, 21-Sep-2004)

	Ref	Expression
Assertion	funcnvcnv	⊢ ( Fun 𝐴 → Fun ◡ ◡ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		cnvcnvss	⊢ ◡ ◡ 𝐴 ⊆ 𝐴
2		funss	⊢ ( ◡ ◡ 𝐴 ⊆ 𝐴 → ( Fun 𝐴 → Fun ◡ ◡ 𝐴 ) )
3	1 2	ax-mp	⊢ ( Fun 𝐴 → Fun ◡ ◡ 𝐴 )