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Theorem pwpwpw0ss 3794
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3727 and pwpw0ss 3791.) (Contributed by Jim Kingdon, 13-Aug-2018.)
Assertion
Ref Expression
pwpwpw0ss ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}

Proof of Theorem pwpwpw0ss
StepHypRef Expression
1 pwprss 3792 1 ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}
Colors of variables: wff set class
Syntax hints:  cun 3119  wss 3121  c0 3414  𝒫 cpw 3566  {csn 3583  {cpr 3584
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 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-dif 3123  df-un 3125  df-in 3127  df-ss 3134  df-nul 3415  df-pw 3568  df-sn 3589  df-pr 3590
This theorem is referenced by: (None)
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