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Theorem pwpwpw0 4833
 Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4744 and pwpw0 4745.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 4831 1 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})
 Colors of variables: wff setvar class Syntax hints:   = wceq 1530   ∪ cun 3938  ∅c0 4295  𝒫 cpw 4542  {csn 4564  {cpr 4566 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2805  df-cleq 2819  df-clel 2898  df-nfc 2968  df-ral 3148  df-v 3502  df-dif 3943  df-un 3945  df-in 3947  df-ss 3956  df-nul 4296  df-pw 4544  df-sn 4565  df-pr 4567 This theorem is referenced by: (None)
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