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Theorem p0ex 3913
Description: The power set of the empty set (the ordinal 1) is a set. (Contributed by NM, 23-Dec-1993.)
Assertion
Ref Expression
p0ex {∅} V

Proof of Theorem p0ex
StepHypRef Expression
1 pw0 3485 . 2 𝒫 ∅ = {∅}
2 0ex 3858 . . 3 V
32pwex 3906 . 2 𝒫 ∅ V
41, 3eqeltrri 2093 1 {∅} V
Colors of variables: wff set class
Syntax hints:   wcel 1374  Vcvv 2535  c0 3201  𝒫 cpw 3334  {csn 3350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 532  ax-in2 533  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-sep 3849  ax-nul 3857  ax-pow 3901
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-dif 2897  df-in 2901  df-ss 2908  df-nul 3202  df-pw 3336  df-sn 3356
This theorem is referenced by:  pp0ex  3914  ordtriexmidlem  4192  onsucsssucexmid  4196  onsucelsucexmid  4199  regexmidlemm  4201  ordsoexmid  4224  opthprc  4318  acexmidlema  5427  acexmidlem2  5433  tposexg  5795
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