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Theorem pwpwpw0 3825
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3762 and pwpw0 3763.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0  |-  ~P { (/)
,  { (/) } }  =  ( { (/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } } )

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 3823 1  |-  ~P { (/)
,  { (/) } }  =  ( { (/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } } )
Colors of variables: wff set class
Syntax hints:    = wceq 1623    u. cun 3150   (/)c0 3455   ~Pcpw 3625   {csn 3640   {cpr 3641
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-pw 3627  df-sn 3646  df-pr 3647
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