MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  funforn Unicode version

Theorem funforn 5474
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.)
Assertion
Ref Expression
funforn  |-  ( Fun 
A  <->  A : dom  A -onto-> ran  A )

Proof of Theorem funforn
StepHypRef Expression
1 funfn 5299 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
2 dffn4 5473 . 2  |-  ( A  Fn  dom  A  <->  A : dom  A -onto-> ran  A )
31, 2bitri 240 1  |-  ( Fun 
A  <->  A : dom  A -onto-> ran  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   dom cdm 4705   ran crn 4706   Fun wfun 5265    Fn wfn 5266   -onto->wfo 5269
This theorem is referenced by:  ordtypelem8  7256  wdomima2g  7316  imadomg  8175  gruima  8440  oppglsm  14969  1stcrestlem  17194  dfac14  17328  qtoptop2  17406  fimacnvinrn  23214
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2289  df-fn 5274  df-fo 5277
  Copyright terms: Public domain W3C validator