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Theorem pwid 4207
 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 4206 . 2 (𝐴 ∈ V → 𝐴 ∈ 𝒫 𝐴)
31, 2ax-mp 5 1 𝐴 ∈ 𝒫 𝐴
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2030  Vcvv 3231  𝒫 cpw 4191 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614  df-ss 3621  df-pw 4193 This theorem is referenced by:  pwnex  7010  r1ordg  8679  rankr1id  8763  cfss  9125  0ram  15771  evl1fval1lem  19742  bastg  20818  fincmp  21244  restlly  21334  ptbasfi  21432  zfbas  21747  ustfilxp  22063  metustfbas  22409  minveclem3b  23245  wilthlem3  24841  coinflipprob  30669  mapdunirnN  37256  pwtrrVD  39374  vsetrec  42774
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