Metamath Proof Explorer

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