ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  f1of1 Unicode version

Theorem f1of1 5125
Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by NM, 12-Dec-2003.)
Assertion
Ref Expression
f1of1  |-  ( F : A -1-1-onto-> B  ->  F : A -1-1-> B )

Proof of Theorem f1of1
StepHypRef Expression
1 df-f1o 4909 . 2  |-  ( F : A -1-1-onto-> B  <->  ( F : A -1-1-> B  /\  F : A -onto-> B ) )
21simplbi 259 1  |-  ( F : A -1-1-onto-> B  ->  F : A -1-1-> B )
Colors of variables: wff set class
Syntax hints:    -> wi 4   -1-1->wf1 4899   -onto->wfo 4900   -1-1-onto->wf1o 4901
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99
This theorem depends on definitions:  df-bi 110  df-f1o 4909
This theorem is referenced by:  f1of  5126  f1oresrab  5329  f1ocnvfvrneq  5422  isores3  5455  isoini2  5458  f1oiso  5465  f1opw2  5706  tposf12  5884  enssdom  6242  phplem4  6318  phplem4on  6329  fidceq  6330
  Copyright terms: Public domain W3C validator