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Theorem dffn3 5396
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 3197 . . 3  |-  ran  F  C_ 
ran  F
21biantru 491 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
ran  F ) )
3 df-f 5259 . 2  |-  ( F : A --> ran  F  <->  ( F  Fn  A  /\  ran  F  C_  ran  F ) )
42, 3bitr4i 243 1  |-  ( F  Fn  A  <->  F : A
--> ran  F )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    C_ wss 3152   ran crn 4690    Fn wfn 5250   -->wf 5251
This theorem is referenced by:  fsn2  5698  fin23lem17  7964  fin23lem32  7970  yoniso  14059  1stckgen  17249  ovolicc2  18881  itg1val2  19039  i1fadd  19050  i1fmul  19051  itg1addlem4  19054  i1fmulc  19058  fnct  23341  ghomgrpilem2  23993  domrancur1c  25202  stoweidlem29  27778  stoweidlem31  27780  stoweidlem59  27808  mapdcl  31843
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-in 3159  df-ss 3166  df-f 5259
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