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Theorem pwid 4626
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 ∈ V
Assertion
Ref Expression
pwid 𝐴 ∈ 𝒫 𝐴

Proof of Theorem pwid
StepHypRef Expression
1 pwid.1 . 2 𝐴 ∈ V
2 pwidg 4624 . 2 (𝐴 ∈ V → 𝐴 ∈ 𝒫 𝐴)
31, 2ax-mp 5 1 𝐴 ∈ 𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  Vcvv 3477  𝒫 cpw 4604
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ss 3979  df-pw 4606
This theorem is referenced by:  pwnex  7777  r1ordg  9815  rankr1id  9899  cfss  10302  0ram  17053  evl1fval1lem  22349  bastg  22988  fincmp  23416  restlly  23506  ptbasfi  23604  zfbas  23919  ustfilxp  24236  minveclem3b  25475  wilthlem3  27127  coinflipprob  34460  mapdunirnN  41632  pwtrrVD  44822  vsetrec  48933
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