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Theorem pp0ex 2761
Description: The power set of the power set of the empty set is a set.
Assertion
Ref Expression
pp0ex |- {(/), {(/)}} e. V
Proof of Theorem pp0ex
StepHypRef Expression
1 pwpw0 2460 . 2 |- P~{(/)} = {(/), {(/)}}
2 p0ex 2760 . . 3 |- {(/)} e. V
32pwex 2735 . 2 |- P~{(/)} e. V
41, 3eqeltrr 1537 1 |- {(/), {(/)}} e. V
Colors of variables: wff set class
Syntax hints:   e. wcel 955  Vcvv 1802  (/)c0 2270  P~cpw 2391  {csn 2399  {cpr 2400
This theorem is referenced by:  zfpair 2767
This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-pow 2732
This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-dif 2039  df-un 2040  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402  df-pr 2403
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