Theorem pwpwpw0 4841

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 4750 and pwpw0 4751.) (Contributed by NM, 2-May-2009.)

Assertion

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

Proof of Theorem pwpwpw0

Step	Hyp	Ref	Expression
1		pwpr 4839	1 ⊢ 𝒫 {∅, {∅}} = ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}})

Syntax hints:   = wceq 1547   ∪ cun 3888  ∅c0 4268  𝒫 cpw 4536  {csn 4562  {cpr 4564

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-ral 3055  df-v 3434  df-dif 3893  df-un 3895  df-in 3897  df-ss 3907  df-nul 4269  df-pw 4538  df-sn 4563  df-pr 4565

This theorem is referenced by: (None)