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Theorem dffn3 5395
Description: A function maps to its range. (Contributed by NM, 1-Sep-1999.)
Assertion
Ref Expression
dffn3  |-  ( F  Fn  A  <->  F : A
--> ran  F )

Proof of Theorem dffn3
StepHypRef Expression
1 ssid 3190 . . 3  |-  ran  F  C_ 
ran  F
21biantru 302 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
ran  F ) )
3 df-f 5239 . 2  |-  ( F : A --> ran  F  <->  ( F  Fn  A  /\  ran  F  C_  ran  F ) )
42, 3bitr4i 187 1  |-  ( F  Fn  A  <->  F : A
--> ran  F )
Colors of variables: wff set class
Syntax hints:    /\ wa 104    <-> wb 105    C_ wss 3144   ran crn 4645    Fn wfn 5230   -->wf 5231
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-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-in 3150  df-ss 3157  df-f 5239
This theorem is referenced by:  fsn2  5710  fo2ndf  6251
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