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Theorem dffn3 5561
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 3331 . . 3  |-  ran  F  C_ 
ran  F
21biantru 492 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
ran  F ) )
3 df-f 5421 . 2  |-  ( F : A --> ran  F  <->  ( F  Fn  A  /\  ran  F  C_  ran  F ) )
42, 3bitr4i 244 1  |-  ( F  Fn  A  <->  F : A
--> ran  F )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    C_ wss 3284   ran crn 4842    Fn wfn 5412   -->wf 5413
This theorem is referenced by:  fsn2  5871  fo2ndf  6416  fin23lem17  8178  fin23lem32  8184  yoniso  14341  1stckgen  17543  ovolicc2  19375  itg1val2  19533  i1fadd  19544  i1fmul  19545  itg1addlem4  19548  i1fmulc  19552  fnct  24062  sibfof  24611  ghomgrpilem2  25054  itg2addnclem2  26160  stoweidlem29  27649  stoweidlem31  27651  stoweidlem59  27679  frgrancvvdeqlemB  28145  mapdcl  32140
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-in 3291  df-ss 3298  df-f 5421
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