Theorem pwpw0ss 3596

Description: Compute the power set of the power set of the empty set. (See pw0 3532 for the power set of the empty set.) Theorem 90 of [Suppes] p. 48 (but with subset in place of equality). (Contributed by Jim Kingdon, 12-Aug-2018.)

Assertion

Ref	Expression
pwpw0ss	⊢ {∅, {∅}} ⊆ 𝒫 {∅}

Proof of Theorem pwpw0ss

Step	Hyp	Ref	Expression
1		pwsnss 3595	1 ⊢ {∅, {∅}} ⊆ 𝒫 {∅}

Syntax hints:   ⊆ wss 2973  ∅c0 3251  𝒫 cpw 3382  {csn 3398  {cpr 3399

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-dif 2975  df-un 2977  df-in 2979  df-ss 2986  df-nul 3252  df-pw 3384  df-sn 3404  df-pr 3405

This theorem is referenced by:  pp0ex  3960