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Theorem pp0ex 4022
Description: {∅, {∅}} (the ordinal 2) is a set. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
pp0ex {∅, {∅}} ∈ V

Proof of Theorem pp0ex
StepHypRef Expression
1 p0ex 4021 . . 3 {∅} ∈ V
21pwex 4016 . 2 𝒫 {∅} ∈ V
3 pwpw0ss 3646 . 2 {∅, {∅}} ⊆ 𝒫 {∅}
42, 3ssexi 3975 1 {∅, {∅}} ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1438  Vcvv 2619  c0 3286  𝒫 cpw 3427  {csn 3444  {cpr 3445
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-sep 3955  ax-nul 3963  ax-pow 4007
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-un 3003  df-in 3005  df-ss 3012  df-nul 3287  df-pw 3429  df-sn 3450  df-pr 3451
This theorem is referenced by:  ord3ex  4023  ontr2exmid  4339  ordtri2or2exmidlem  4340  onsucelsucexmidlem  4343  regexmid  4349  reg2exmid  4350  reg3exmid  4393  nnregexmid  4432  acexmidlemcase  5639  acexmidlemv  5642
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