Theorem pwpwpw0 4908

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4820 and pwpw0 4821.) (Contributed by NM, 2-May-2009.)

Assertion

Ref	Expression
pwpwpw0	⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Proof of Theorem pwpwpw0

Step	Hyp	Ref	Expression
1		pwpr 4906	1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Syntax hints:   = wceq 1533   ∪ cun 3944  ∅c0 4324  𝒫 cpw 4606  {csn 4632  {cpr 4634

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-ral 3051  df-v 3463  df-dif 3949  df-un 3951  df-in 3953  df-ss 3963  df-nul 4325  df-pw 4608  df-sn 4633  df-pr 4635

This theorem is referenced by: (None)