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