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Theorem pwpwpw0 4908
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4817 and pwpw0 4818.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 4906 1 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  cun 3961  c0 4339  𝒫 cpw 4605  {csn 4631  {cpr 4633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-pw 4607  df-sn 4632  df-pr 4634
This theorem is referenced by: (None)
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