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Theorem abssexg 3925
Description: Existence of a class of subsets. (Contributed by NM, 15-Jul-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
abssexg  V  {  |  C_  }  _V
Distinct variable group:   ,
Allowed substitution hints:   ()    V()

Proof of Theorem abssexg
StepHypRef Expression
1 pwexg 3924 . 2  V  ~P  _V
2 df-pw 3353 . . . 4  ~P  {  | 
C_  }
32eleq1i 2100 . . 3  ~P  _V  {  |  C_  }  _V
4 simpl 102 . . . . 5  C_  C_
54ss2abi 3006 . . . 4  {  |  C_  }  C_  {  |  C_  }
6 ssexg 3887 . . . 4  {  |  C_  }  C_  {  |  C_  }  {  | 
C_  }  _V  {  |  C_  }  _V
75, 6mpan 400 . . 3  {  |  C_  }  _V  {  | 
C_  }  _V
83, 7sylbi 114 . 2  ~P  _V  {  | 
C_  }  _V
91, 8syl 14 1  V  {  |  C_  }  _V
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wcel 1390   {cab 2023   _Vcvv 2551    C_ wss 2911   ~Pcpw 3351
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-bndl 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
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-pw 3353
This theorem is referenced by: (None)
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