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Theorem dffn3 5627
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 3353 . . 3  |-  ran  F  C_ 
ran  F
21biantru 493 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
ran  F ) )
3 df-f 5487 . 2  |-  ( F : A --> ran  F  <->  ( F  Fn  A  /\  ran  F  C_  ran  F ) )
42, 3bitr4i 245 1  |-  ( F  Fn  A  <->  F : A
--> ran  F )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    C_ wss 3306   ran crn 4908    Fn wfn 5478   -->wf 5479
This theorem is referenced by:  fsn2  5937  fo2ndf  6482  fin23lem17  8249  fin23lem32  8255  yoniso  14413  1stckgen  17617  ovolicc2  19449  itg1val2  19605  i1fadd  19616  i1fmul  19617  itg1addlem4  19620  i1fmulc  19624  fnct  24136  sibfof  24685  ghomgrpilem2  25128  itg2addnclem2  26295  stoweidlem29  27792  stoweidlem31  27794  stoweidlem59  27822  frgrancvvdeqlemB  28525  mapdcl  32549
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-in 3313  df-ss 3320  df-f 5487
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