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Theorem pwex 4227
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 4224 . 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 2176   _Vcvv 2772   ~Pcpw 3616
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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-14 2179  ax-ext 2187  ax-sep 4162  ax-pow 4218
This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-in 3172  df-ss 3179  df-pw 3618
This theorem is referenced by:  p0ex  4232  pp0ex  4233  ord3ex  4234  abexssex  6210  fnpm  6743  exmidpw  7005  pw1on  7338  pw1dom2  7339  pw1nel3  7343  sucpw1ne3  7344  sucpw1nel3  7345  npex  7586  axcnex  7972  pnfxr  8125  mnfxr  8129  ixxex  10021  prdsvallem  13104  istopon  14485  dmtopon  14495  fncld  14570
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