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Theorem pwex 4226
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 4223 . 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 2175   _Vcvv 2771   ~Pcpw 3615
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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-14 2178  ax-ext 2186  ax-sep 4161  ax-pow 4217
This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-in 3171  df-ss 3178  df-pw 3617
This theorem is referenced by:  p0ex  4231  pp0ex  4232  ord3ex  4233  abexssex  6209  fnpm  6742  exmidpw  7004  pw1on  7337  pw1dom2  7338  pw1nel3  7342  sucpw1ne3  7343  sucpw1nel3  7344  npex  7585  axcnex  7971  pnfxr  8124  mnfxr  8128  ixxex  10020  prdsvallem  13075  istopon  14456  dmtopon  14466  fncld  14541
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