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Theorem pwid 4536
 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 4534 . 2 (𝐴 ∈ V → 𝐴 ∈ 𝒫 𝐴)
31, 2ax-mp 5 1 𝐴 ∈ 𝒫 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2115  Vcvv 3471  𝒫 cpw 4512 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2178  ax-ext 2793 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2800  df-cleq 2814  df-clel 2892  df-nfc 2960  df-v 3473  df-in 3917  df-ss 3927  df-pw 4514 This theorem is referenced by:  pwnex  7456  r1ordg  9183  rankr1id  9267  cfss  9664  0ram  16333  evl1fval1lem  20469  bastg  21550  fincmp  21977  restlly  22067  ptbasfi  22165  zfbas  22480  ustfilxp  22797  minveclem3b  24011  wilthlem3  25634  coinflipprob  31745  mapdunirnN  38832  pwtrrVD  41346  vsetrec  45043
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