Metamath Proof Explorer

Theorem f1ofo

Description: A one-to-one onto function is an onto function. (Contributed by NM, 28-Apr-2004)

Ref Expression
Assertion f1ofo 
|- ( F : A -1-1-onto-> B -> F : A -onto-> B )

Proof

Step Hyp Ref Expression
1 dff1o3 
 |-  ( F : A -1-1-onto-> B <-> ( F : A -onto-> B /\ Fun `' F ) )
2 1 simplbi 
 |-  ( F : A -1-1-onto-> B -> F : A -onto-> B )