Theorem pwpwpw0ss 3854

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3786 and pwpw0ss 3851.) (Contributed by Jim Kingdon, 13-Aug-2018.)

Assertion

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

Proof of Theorem pwpwpw0ss

Step	Hyp	Ref	Expression
1		pwprss 3852	1 |- ( { (/) , { (/) } } u. { { { (/) } } , { (/) , { (/) } } } ) C_ ~P { (/) , { (/) } }

Syntax hints:   u. cun 3168   C_ wss 3170   (/)c0 3464   ~Pcpw 3621   {csn 3638   {cpr 3639

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-dif 3172  df-un 3174  df-in 3176  df-ss 3183  df-nul 3465  df-pw 3623  df-sn 3644  df-pr 3645

This theorem is referenced by: (None)