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Theorem pwex 4169
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 4166 . 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 2141   _Vcvv 2730   ~Pcpw 3566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-14 2144  ax-ext 2152  ax-sep 4107  ax-pow 4160
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-in 3127  df-ss 3134  df-pw 3568
This theorem is referenced by:  p0ex  4174  pp0ex  4175  ord3ex  4176  abexssex  6104  fnpm  6634  exmidpw  6886  pw1on  7203  pw1dom2  7204  pw1nel3  7208  sucpw1ne3  7209  sucpw1nel3  7210  npex  7435  axcnex  7821  pnfxr  7972  mnfxr  7976  ixxex  9856  istopon  12805  dmtopon  12815  fncld  12892
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