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Theorem funforn 5441
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 5242 . 2  |-  ( Fun 
A  <->  A  Fn  dom  A )
2 dffn4 5440 . 2  |-  ( A  Fn  dom  A  <->  A : dom  A -onto-> ran  A )
31, 2bitri 184 1  |-  ( Fun 
A  <->  A : dom  A -onto-> ran  A )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   dom cdm 4623   ran crn 4624   Fun wfun 5206    Fn wfn 5207   -onto->wfo 5210
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1449  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-fn 5215  df-fo 5218
This theorem is referenced by:  dvrecap  13841
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