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Theorem pwpwpw0 4540
 Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4451 and pwpw0 4452.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 4538 1 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})
 Colors of variables: wff setvar class Syntax hints:   = wceq 1596   ∪ cun 3678  ∅c0 4023  𝒫 cpw 4266  {csn 4285  {cpr 4287 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-ral 3019  df-v 3306  df-dif 3683  df-un 3685  df-in 3687  df-ss 3694  df-nul 4024  df-pw 4268  df-sn 4286  df-pr 4288 This theorem is referenced by: (None)
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