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Theorem pwid 4554
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 4552 . 2 (𝐴 ∈ V → 𝐴 ∈ 𝒫 𝐴)
31, 2ax-mp 5 1 𝐴 ∈ 𝒫 𝐴
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  Vcvv 3422  𝒫 cpw 4530
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-pw 4532
This theorem is referenced by:  pwnex  7587  r1ordg  9467  rankr1id  9551  cfss  9952  0ram  16649  evl1fval1lem  21406  bastg  22024  fincmp  22452  restlly  22542  ptbasfi  22640  zfbas  22955  ustfilxp  23272  minveclem3b  24497  wilthlem3  26124  coinflipprob  32346  mapdunirnN  39591  pwtrrVD  42334  vsetrec  46294
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