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Theorem mptfng 4967
Description: The maps-to notation defines a function with domain. (Contributed by Scott Fenton, 21-Mar-2011.)
Hypothesis
Ref Expression
mptfng.1  F  |->
Assertion
Ref Expression
mptfng  _V  F  Fn
Distinct variable group:   ,
Allowed substitution hints:   ()    F()

Proof of Theorem mptfng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eueq 2706 . . 3  _V
21ralbii 2324 . 2  _V
3 mptfng.1 . . . 4  F  |->
4 df-mpt 3811 . . . 4  |->  { <. ,  >.  |  }
53, 4eqtri 2057 . . 3  F  { <. , 
>.  |  }
65fnopabg 4965 . 2  F  Fn
72, 6bitri 173 1  _V  F  Fn
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98   wceq 1242   wcel 1390  weu 1897  wral 2300   _Vcvv 2551   {copab 3808    |-> cmpt 3809    Fn wfn 4840
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-mpt 3811  df-id 4021  df-xp 4294  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-fun 4847  df-fn 4848
This theorem is referenced by:  fnmpt  4968  fnmpti  4970  mpteqb  5204
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