Metamath Proof Explorer


Theorem ffun

Description: A mapping is a function. (Contributed by NM, 3-Aug-1994) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion ffun ( 𝐹 : 𝐴 ⟶ 𝐵 → Fun 𝐹 )

Proof

Step Hyp Ref Expression
1 ffn ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → 𝐹 Fn 𝐴 )
2 1 fnfund ⊢ ( 𝐹 : 𝐴 ⟶ 𝐵 → Fun 𝐹 )