Theorem pwpwpw0ss 3657

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3590 and pwpw0ss 3654.) (Contributed by Jim Kingdon, 13-Aug-2018.)

Assertion

Ref	Expression
pwpwpw0ss	|- ( { (/) , { (/) } } u. { { { (/) } } , { (/) , { (/) } } } ) C_ ~P { (/) , { (/) } }

Proof of Theorem pwpwpw0ss

Step	Hyp	Ref	Expression
1		pwprss 3655	1 |- ( { (/) , { (/) } } u. { { { (/) } } , { (/) , { (/) } } } ) C_ ~P { (/) , { (/) } }

Syntax hints:   u. cun 2998   C_ wss 3000   (/)c0 3287   ~Pcpw 3433   {csn 3450   {cpr 3451

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-dif 3002  df-un 3004  df-in 3006  df-ss 3013  df-nul 3288  df-pw 3435  df-sn 3456  df-pr 3457

This theorem is referenced by: (None)