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Theorem pwpw0ss 3735
Description: Compute the power set of the power set of the empty set. (See pw0 3671 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 3734 1 {∅, {∅}} ⊆ 𝒫 {∅}
Colors of variables: wff set class
Syntax hints:  wss 3072  c0 3364  𝒫 cpw 3511  {csn 3528  {cpr 3529
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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-dif 3074  df-un 3076  df-in 3078  df-ss 3085  df-nul 3365  df-pw 3513  df-sn 3534  df-pr 3535
This theorem is referenced by:  pp0ex  4117  exmidpw  6806  pw1dom2  13344
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