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Theorem pwpwpw0ss 3569
Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3502 and pwpw0ss 3566.) (Contributed by Jim Kingdon, 13-Aug-2018.)
Assertion
Ref Expression
pwpwpw0ss  { (/)
,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } }  C_  ~P { (/) ,  { (/) } }

Proof of Theorem pwpwpw0ss
StepHypRef Expression
1 pwprss 3567 1  { (/)
,  { (/) } }  u.  { { { (/) } } ,  { (/) ,  { (/) } } }  C_  ~P { (/) ,  { (/) } }
Colors of variables: wff set class
Syntax hints:    u. cun 2909    C_ wss 2911   (/)c0 3218   ~Pcpw 3351   {csn 3367   {cpr 3368
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-dif 2914  df-un 2916  df-in 2918  df-ss 2925  df-nul 3219  df-pw 3353  df-sn 3373  df-pr 3374
This theorem is referenced by: (None)
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