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Theorem dffn2 5592
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 3368 . . 3  |-  ran  F  C_ 
_V
21biantru 492 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
3 df-f 5458 . 2  |-  ( F : A --> _V  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
42, 3bitr4i 244 1  |-  ( F  Fn  A  <->  F : A
--> _V )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359   _Vcvv 2956    C_ wss 3320   ran crn 4879    Fn wfn 5449   -->wf 5450
This theorem is referenced by:  f1cnvcnv  5647  fcoconst  5905  fnressn  5918  1stcof  6374  2ndcof  6375  fnmpt2  6419  tposfn  6508  tz7.48lem  6698  seqomlem2  6708  mptelixpg  7099  r111  7701  smobeth  8461  inar1  8650  imasvscafn  13762  fucidcl  14162  fucsect  14169  curfcl  14329  curf2ndf  14344  prdstopn  17660  prdstps  17661  ist0-4  17761  ptuncnv  17839  xpstopnlem2  17843  prdstgpd  18154  prdsxmslem2  18559  curry2ima  24097  fndifnfp  26737  dsmmbas2  27180  frlmsslsp  27225  frlmup1  27227  fnchoice  27676  stoweidlem35  27760
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958  df-in 3327  df-ss 3334  df-f 5458
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