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Theorem p0ex 4639
Description: The power set of the empty set (the ordinal 1) is a set. See also p0exALT 4640. (Contributed by NM, 23-Dec-1993.)
Assertion
Ref Expression
p0ex

Proof of Theorem p0ex
StepHypRef Expression
1 pw0 4177 . 2
2 0ex 4582 . . 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
This theorem is referenced by:  pp0ex  4641  dtruALT  4684  zfpair  4689  snsn0non  5001  opthprc  5052  fvclex  6772  tposexg  6988  2dom  7608  map1  7614  endisj  7624  pw2eng  7643  dfac4  8524  dfac2  8532  cdaval  8571  axcc2lem  8837  axdc2lem  8849  axcclem  8858  axpowndlem3  8996  axpowndlem3OLD  8997  ccatfn  12591  isstruct2  14641  plusffval  15877  staffval  17496  scaffval  17530  lpival  17893  ipffval  18683  refun0  20016  filcon  20384  alexsubALTlem2  20548  nmfval  21109  tchex  21660  tchnmfval  21671  legval  23971  locfinref  27844  oms0  28266  rankeq1o  29828  ssoninhaus  29913  onint1  29914  rrnval  30323  dvnprodlem3  31745  bnj105  33777  bj-tagex  34545  bj-1uplex  34566  lsatset  34715
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-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-in 3482  df-ss 3489  df-nul 3785  df-pw 4014  df-sn 4030
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