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Theorem pwpwpw0ss 3625
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3558 and pwpw0ss 3622.) (Contributed by Jim Kingdon, 13-Aug-2018.)
Assertion
Ref Expression
pwpwpw0ss ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}

Proof of Theorem pwpwpw0ss
StepHypRef Expression
1 pwprss 3623 1 ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}
Colors of variables: wff set class
Syntax hints:  cun 2982  wss 2984  c0 3269  𝒫 cpw 3406  {csn 3422  {cpr 3423
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 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-dif 2986  df-un 2988  df-in 2990  df-ss 2997  df-nul 3270  df-pw 3408  df-sn 3428  df-pr 3429
This theorem is referenced by: (None)
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