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Theorem pp0ex 4207
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 4206 . . 3 {∅} ∈ V
21pwex 4201 . 2 𝒫 {∅} ∈ V
3 pwpw0ss 3819 . 2 {∅, {∅}} ⊆ 𝒫 {∅}
42, 3ssexi 4156 1 {∅, {∅}} ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2160  Vcvv 2752  c0 3437  𝒫 cpw 3590  {csn 3607  {cpr 3608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-nul 4144  ax-pow 4192
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157  df-nul 3438  df-pw 3592  df-sn 3613  df-pr 3614
This theorem is referenced by:  ord3ex  4208  ontr2exmid  4542  ordtri2or2exmidlem  4543  onsucelsucexmidlem  4546  regexmid  4552  reg2exmid  4553  reg3exmid  4597  nnregexmid  4638  acexmidlemcase  5892  acexmidlemv  5895  exmidpw2en  6941  exmidaclem  7238
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