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Theorem pwpwpw0 4906
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4818 and pwpw0 4819.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 4904 1 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  cun 3945  c0 4324  𝒫 cpw 4604  {csn 4630  {cpr 4632
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 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-ral 3058  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-pw 4606  df-sn 4631  df-pr 4633
This theorem is referenced by: (None)
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