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Theorem funforn 5662
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 5484 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
2 dffn4 5661 . 2  |-  ( A  Fn  dom  A  <->  A : dom  A -onto-> ran  A )
31, 2bitri 242 1  |-  ( Fun 
A  <->  A : dom  A -onto-> ran  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 178   dom cdm 4880   ran crn 4881   Fun wfun 5450    Fn wfn 5451   -onto->wfo 5454
This theorem is referenced by:  ordtypelem8  7496  wdomima2g  7556  imadomg  8414  gruima  8679  oppglsm  15278  1stcrestlem  17517  dfac14  17652  qtoptop2  17733  fimacnvinrn  24049
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-cleq 2431  df-fn 5459  df-fo 5462
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