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Theorem pwex 4009
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 4007 . 2  |-  ( A  e.  _V  ->  ~P A  e.  _V )
31, 2ax-mp 7 1  |-  ~P A  e.  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   _Vcvv 2619   ~Pcpw 3425
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3949  ax-pow 4001
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3003  df-ss 3010  df-pw 3427
This theorem is referenced by:  p0ex  4014  pp0ex  4015  ord3ex  4016  abexssex  5878  fnpm  6393  exmidpw  6604  npex  7011  axcnex  7375  pnfxr  7519  mnfxr  7523  ixxex  9286  pw1dom2  11546
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