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Theorem funforn 5458
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 5283 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
2 dffn4 5457 . 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 4689   ran crn 4690   Fun wfun 5249    Fn wfn 5250   -onto->wfo 5253
This theorem is referenced by:  ordtypelem8  7240  wdomima2g  7300  imadomg  8159  gruima  8424  oppglsm  14953  1stcrestlem  17178  dfac14  17312  qtoptop2  17390  fimacnvinrn  23199
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-cleq 2276  df-fn 5258  df-fo 5261
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