Theorem elfunsg

Description: Closed form of elfuns . (Contributed by Scott Fenton, 2-May-2014)

	Ref	Expression
Assertion	elfunsg	⊢ ( 𝐹 ∈ 𝑉 → ( 𝐹 ∈ Funs ↔ Fun 𝐹 ) )

Proof

Step	Hyp	Ref	Expression
1		eleq1	⊢ ( 𝑓 = 𝐹 → ( 𝑓 ∈ Funs ↔ 𝐹 ∈ Funs ) )
2		funeq	⊢ ( 𝑓 = 𝐹 → ( Fun 𝑓 ↔ Fun 𝐹 ) )
3		vex	⊢ 𝑓 ∈ V
4	3	elfuns	⊢ ( 𝑓 ∈ Funs ↔ Fun 𝑓 )
5	1 2 4	vtoclbg	⊢ ( 𝐹 ∈ 𝑉 → ( 𝐹 ∈ Funs ↔ Fun 𝐹 ) )