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Theorem pwid 3598
Description: A set is a member of its power class. Theorem 87 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
pwid.1  |-  A  e. 
_V
Assertion
Ref Expression
pwid  |-  A  e. 
~P A

Proof of Theorem pwid
StepHypRef Expression
1 pwid.1 . 2  |-  A  e. 
_V
2 pwidg 3597 . 2  |-  ( A  e.  _V  ->  A  e.  ~P A )
31, 2ax-mp 10 1  |-  A  e. 
~P A
Colors of variables: wff set class
Syntax hints:    e. wcel 1621   _Vcvv 2757   ~Pcpw 3585
This theorem is referenced by:  r1ordg  7404  rankr1id  7488  cfss  7845  0ram  13015  bastg  16652  fincmp  17068  restlly  17157  ptbasfi  17224  zfbas  17539  minveclem3b  18740  wilthlem3  20256  nZdef  24533  pwtrrVD  27634  pwtrrOLD  27635  mapdunirnN  30991
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2759  df-in 3120  df-ss 3127  df-pw 3587
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