Theorem pwpwpw0ss 3772

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 3705 and pwpw0ss 3769.) (Contributed by Jim Kingdon, 13-Aug-2018.)

Assertion

Ref	Expression
pwpwpw0ss	⊢ ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}

Proof of Theorem pwpwpw0ss

Step	Hyp	Ref	Expression
1		pwprss 3770	1 ⊢ ({∅, {∅}} ∪ {{{∅}}, {∅, {∅}}}) ⊆ 𝒫 {∅, {∅}}

Syntax hints:   ∪ cun 3100   ⊆ wss 3102  ∅c0 3395  𝒫 cpw 3544  {csn 3561  {cpr 3562

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-dif 3104  df-un 3106  df-in 3108  df-ss 3115  df-nul 3396  df-pw 3546  df-sn 3567  df-pr 3568

This theorem is referenced by: (None)