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Theorem funforn 5358
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 5159 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
2 dffn4 5357 . 2  |-  ( A  Fn  dom  A  <->  A : dom  A -onto-> ran  A )
31, 2bitri 183 1  |-  ( Fun 
A  <->  A : dom  A -onto-> ran  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 104   dom cdm 4545   ran crn 4546   Fun wfun 5123    Fn wfn 5124   -onto->wfo 5127
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1426  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-fn 5132  df-fo 5135
This theorem is referenced by:  dvrecap  12878
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