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Theorem dffn2 5078
Description: Any function is a mapping into  _V. (Contributed by NM, 31-Oct-1995.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
dffn2  |-  ( F  Fn  A  <->  F : A
--> _V )

Proof of Theorem dffn2
StepHypRef Expression
1 ssv 3020 . . 3  |-  ran  F  C_ 
_V
21biantru 296 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
3 df-f 4936 . 2  |-  ( F : A --> _V  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
42, 3bitr4i 185 1  |-  ( F  Fn  A  <->  F : A
--> _V )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   _Vcvv 2602    C_ wss 2974   ran crn 4372    Fn wfn 4927   -->wf 4928
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-v 2604  df-in 2980  df-ss 2987  df-f 4936
This theorem is referenced by:  f1cnvcnv  5131  fcoconst  5366  fnressn  5381  1stcof  5821  2ndcof  5822  fnmpt2  5859  tposfn  5922  tfrlemibfn  5977  tfr1onlembfn  5993
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