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Theorem pwpwpw0 4015
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3947 and pwpw0 3948.) (Contributed by NM, 2-May-2009.)
Assertion
Ref Expression
pwpwpw0  |-  ~P { (/)
,  { (/) } }  =  ( { (/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } } )

Proof of Theorem pwpwpw0
StepHypRef Expression
1 pwpr 4013 1  |-  ~P { (/)
,  { (/) } }  =  ( { (/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } } )
Colors of variables: wff set class
Syntax hints:    = wceq 1653    u. cun 3320   (/)c0 3630   ~Pcpw 3801   {csn 3816   {cpr 3817
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-pw 3803  df-sn 3822  df-pr 3823
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