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Theorem pp0ex 4641
 Description: The power set of the power set of the empty set (the ordinal 2) is a set. (Contributed by NM, 24-Jun-1993.)
Assertion
Ref Expression
pp0ex

Proof of Theorem pp0ex
StepHypRef Expression
1 pwpw0 4178 . 2
2 p0ex 4639 . . 3
32pwex 4635 . 2
41, 3eqeltrri 2542 1
 Colors of variables: wff setvar class Syntax hints:  e.wcel 1818   cvv 3109   c0 3784  ~Pcpw 4012  {csn 4029  {cpr 4031 This theorem is referenced by:  ord3ex  4642  zfpair  4689 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030  df-pr 4032
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