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Theorem dffn2 5349
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 3169 . . 3  |-  ran  F  C_ 
_V
21biantru 300 . 2  |-  ( F  Fn  A  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
3 df-f 5202 . 2  |-  ( F : A --> _V  <->  ( F  Fn  A  /\  ran  F  C_ 
_V ) )
42, 3bitr4i 186 1  |-  ( F  Fn  A  <->  F : A
--> _V )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   _Vcvv 2730    C_ wss 3121   ran crn 4612    Fn wfn 5193   -->wf 5194
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732  df-in 3127  df-ss 3134  df-f 5202
This theorem is referenced by:  f1cnvcnv  5414  fcoconst  5667  fnressn  5682  1stcof  6142  2ndcof  6143  fnmpo  6181  tposfn  6252  tfrlemibfn  6307  tfr1onlembfn  6323  mptelixpg  6712
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