Metamath Proof Explorer

Theorem f1fun

Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion f1fun 
|- ( F : A -1-1-> B -> Fun F )

Proof

Step Hyp Ref Expression
1 f1fn 
 |-  ( F : A -1-1-> B -> F Fn A )
2 1 fnfund 
 |-  ( F : A -1-1-> B -> Fun F )