Theorem pwpwpw0 4432

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4343 and pwpw0 4344.) (Contributed by NM, 2-May-2009.)

Assertion

Ref	Expression
pwpwpw0	|- ~P { (/) , { (/) } } = ( { (/) , { (/) } } u. { { { (/) } } , { (/) , { (/) } } } )

Proof of Theorem pwpwpw0

Step	Hyp	Ref	Expression
1		pwpr 4430	1 |- ~P { (/) , { (/) } } = ( { (/) , { (/) } } u. { { { (/) } } , { (/) , { (/) } } } )

Syntax hints:   = wceq 1483   u. cun 3572   (/)c0 3915   ~Pcpw 4158   {csn 4177   {cpr 4179

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ral 2917  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-pw 4160  df-sn 4178  df-pr 4180

This theorem is referenced by: (None)