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Theorem pp0ex 4083
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 4082 . . 3 {∅} ∈ V
21pwex 4077 . 2 𝒫 {∅} ∈ V
3 pwpw0ss 3701 . 2 {∅, {∅}} ⊆ 𝒫 {∅}
42, 3ssexi 4036 1 {∅, {∅}} ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1465  Vcvv 2660  c0 3333  𝒫 cpw 3480  {csn 3497  {cpr 3498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-14 1477  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-nul 4024  ax-pow 4068
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043  df-un 3045  df-in 3047  df-ss 3054  df-nul 3334  df-pw 3482  df-sn 3503  df-pr 3504
This theorem is referenced by:  ord3ex  4084  ontr2exmid  4410  ordtri2or2exmidlem  4411  onsucelsucexmidlem  4414  regexmid  4420  reg2exmid  4421  reg3exmid  4464  nnregexmid  4504  acexmidlemcase  5737  acexmidlemv  5740  exmidaclem  7032
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