ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwex Unicode version

Theorem pwex 4144
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 4141 . 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 2128   _Vcvv 2712   ~Pcpw 3543
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4135
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-ss 3115  df-pw 3545
This theorem is referenced by:  p0ex  4149  pp0ex  4150  ord3ex  4151  abexssex  6073  fnpm  6601  exmidpw  6853  pw1on  7161  pw1dom2  7162  pw1nel3  7166  sucpw1ne3  7167  sucpw1nel3  7168  npex  7393  axcnex  7779  pnfxr  7930  mnfxr  7934  ixxex  9803  istopon  12422  dmtopon  12432  fncld  12509
  Copyright terms: Public domain W3C validator