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Theorem pwpwpw0ss 3607
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3540 and pwpw0ss 3604.) (Contributed by Jim Kingdon, 13-Aug-2018.)
Assertion
Ref Expression
pwpwpw0ss  |-  ( {
(/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } }
)  C_  ~P { (/) ,  { (/) } }

Proof of Theorem pwpwpw0ss
StepHypRef Expression
1 pwprss 3605 1  |-  ( {
(/) ,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } }
)  C_  ~P { (/) ,  { (/) } }
Colors of variables: wff set class
Syntax hints:    u. cun 2972    C_ wss 2974   (/)c0 3258   ~Pcpw 3390   {csn 3406   {cpr 3407
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-un 2978  df-in 2980  df-ss 2987  df-nul 3259  df-pw 3392  df-sn 3412  df-pr 3413
This theorem is referenced by: (None)
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