Theorem structfun

Description: Convert between two kinds of structure closure. (Contributed by Mario Carneiro, 29-Aug-2015) (Proof shortened by AV, 12-Nov-2021)

	Ref	Expression
Hypothesis	structfun.1	⊢ 𝐹 Struct 𝑋
Assertion	structfun	⊢ Fun ◡ ◡ 𝐹

Proof

Step	Hyp	Ref	Expression
1		structfun.1	⊢ 𝐹 Struct 𝑋
2		structfung	⊢ ( 𝐹 Struct 𝑋 → Fun ◡ ◡ 𝐹 )
3	1 2	ax-mp	⊢ Fun ◡ ◡ 𝐹