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Metamath Proof Explorer

Theorem fofun

Description: An onto mapping is a function. (Contributed by NM, 29-Mar-2008)

Ref Expression
Assertion fofun ( 𝐹 : 𝐴 –onto→ 𝐵 → Fun 𝐹 )

Proof

Step Hyp Ref Expression
1 fof ⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐵 )
2 1 ffund ⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → Fun 𝐹 )