Metamath Proof Explorer

Theorem f1f

Description: A one-to-one mapping is a mapping. (Contributed by NM, 31-Dec-1996)

Ref Expression
Assertion f1f 
|- ( F : A -1-1-> B -> F : A --> B )

Proof

Step Hyp Ref Expression
1 df-f1 
 |-  ( F : A -1-1-> B <-> ( F : A --> B /\ Fun `' F ) )
2 1 simplbi 
 |-  ( F : A -1-1-> B -> F : A --> B )