Metamath Proof Explorer

Theorem f1of1

Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by NM, 12-Dec-2003)

Ref Expression
Assertion f1of1 
|- ( F : A -1-1-onto-> B -> F : A -1-1-> B )

Proof

Step Hyp Ref Expression
1 df-f1o 
 |-  ( F : A -1-1-onto-> B <-> ( F : A -1-1-> B /\ F : A -onto-> B ) )
2 1 simplbi 
 |-  ( F : A -1-1-onto-> B -> F : A -1-1-> B )