Theorem fnfun

Description: A function with domain is a function. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Assertion	fnfun	⊢ ( 𝐹 Fn 𝐴 → Fun 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		df-fn	⊢ ( 𝐹 Fn 𝐴 ↔ ( Fun 𝐹 ∧ dom 𝐹 = 𝐴 ) )
2	1	simplbi	⊢ ( 𝐹 Fn 𝐴 → Fun 𝐹 )