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Theorem pwpw0ss 3598
 Description: Compute the power set of the power set of the empty set. (See pw0 3534 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
StepHypRef Expression
1 pwsnss 3597 1 {∅, {∅}} ⊆ 𝒫 {∅}
 Colors of variables: wff set class Syntax hints:   ⊆ wss 2974  ∅c0 3252  𝒫 cpw 3384  {csn 3400  {cpr 3401 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 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-dif 2976  df-un 2978  df-in 2980  df-ss 2987  df-nul 3253  df-pw 3386  df-sn 3406  df-pr 3407 This theorem is referenced by:  pp0ex  3962
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