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Theorem pwex 4201
Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
pwex.1  |-  A  e. 
_V
Assertion
Ref Expression
pwex  |-  ~P A  e.  _V

Proof of Theorem pwex
StepHypRef Expression
1 pwex.1 . 2  |-  A  e. 
_V
2 pwexg 4198 . 2  |-  ( A  e.  _V  ->  ~P A  e.  _V )
31, 2ax-mp 5 1  |-  ~P A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 2160   _Vcvv 2752   ~Pcpw 3590
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4192
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150  df-ss 3157  df-pw 3592
This theorem is referenced by:  p0ex  4206  pp0ex  4207  ord3ex  4208  abexssex  6150  fnpm  6682  exmidpw  6936  pw1on  7255  pw1dom2  7256  pw1nel3  7260  sucpw1ne3  7261  sucpw1nel3  7262  npex  7502  axcnex  7888  pnfxr  8040  mnfxr  8044  ixxex  9929  istopon  13970  dmtopon  13980  fncld  14055
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