Metamath Proof Explorer


Theorem f1fn

Description: A one-to-one mapping is a function on its domain. (Contributed by NM, 8-Mar-2014)

Ref Expression
Assertion f1fn ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 Fn 𝐴 )

Proof

Step Hyp Ref Expression
1 f1f ⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐵 )
2 1 ffnd ⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 Fn 𝐴 )