ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dffn4 Unicode version

Theorem dffn4 5143
Description: A function maps onto its range. (Contributed by NM, 10-May-1998.)
Assertion
Ref Expression
dffn4  |-  ( F  Fn  A  <->  F : A -onto-> ran  F )

Proof of Theorem dffn4
StepHypRef Expression
1 eqid 2082 . . 3  |-  ran  F  =  ran  F
21biantru 296 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  =  ran  F ) )
3 df-fo 4938 . 2  |-  ( F : A -onto-> ran  F  <->  ( F  Fn  A  /\  ran  F  =  ran  F
) )
42, 3bitr4i 185 1  |-  ( F  Fn  A  <->  F : A -onto-> ran  F )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103    = wceq 1285   ran crn 4372    Fn wfn 4927   -onto->wfo 4930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-fo 4938
This theorem is referenced by:  funforn  5144  ffoss  5189  tposf2  5917
  Copyright terms: Public domain W3C validator