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Theorem pwpw0ss 3802
Description: Compute the power set of the power set of the empty set. (See pw0 3738 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 3801 1  |-  { (/) ,  { (/) } }  C_  ~P { (/) }
Colors of variables: wff set class
Syntax hints:    C_ wss 3129   (/)c0 3422   ~Pcpw 3574   {csn 3591   {cpr 3592
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-un 3133  df-in 3135  df-ss 3142  df-nul 3423  df-pw 3576  df-sn 3597  df-pr 3598
This theorem is referenced by:  pp0ex  4186  exmidpw  6901  exmidpweq  6902  pw1dom2  7219  pw1ne1  7221
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