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Theorem pwid 3735
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 A

Proof of Theorem pwid
StepHypRef Expression
1 pwid.1 . 2 A V
2 pwidg 3734 . 2 (A V → A A)
31, 2ax-mp 5 1 A A
Colors of variables: wff setvar class
Syntax hints:   wcel 1710  Vcvv 2859  cpw 3722
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-pw 3724
This theorem is referenced by: (None)
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