ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwpw0ss Unicode version

Theorem pwpw0ss 3701
Description: Compute the power set of the power set of the empty set. (See pw0 3637 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  |-  { (/) ,  { (/) } }  C_  ~P { (/) }

Proof of Theorem pwpw0ss
StepHypRef Expression
1 pwsnss 3700 1  |-  { (/) ,  { (/) } }  C_  ~P { (/) }
Colors of variables: wff set class
Syntax hints:    C_ wss 3041   (/)c0 3333   ~Pcpw 3480   {csn 3497   {cpr 3498
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043  df-un 3045  df-in 3047  df-ss 3054  df-nul 3334  df-pw 3482  df-sn 3503  df-pr 3504
This theorem is referenced by:  pp0ex  4083  exmidpw  6770  pw1dom2  13117
  Copyright terms: Public domain W3C validator