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Theorem 0nep0 5223
 Description: The empty set and its power set are not equal. (Contributed by NM, 23-Dec-1993.)
Assertion
Ref Expression
0nep0 ∅ ≠ {∅}

Proof of Theorem 0nep0
StepHypRef Expression
1 0ex 5175 . . 3 ∅ ∈ V
21snnz 4672 . 2 {∅} ≠ ∅
32necomi 3041 1 ∅ ≠ {∅}
 Colors of variables: wff setvar class Syntax hints:   ≠ wne 2987  ∅c0 4243  {csn 4525 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-nul 5174 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-v 3443  df-dif 3884  df-nul 4244  df-sn 4526 This theorem is referenced by:  0inp0  5224  opthprc  5580  2dom  8567  pw2eng  8608  djuexb  9324  hashge3el3dif  13842  isusp  22874  bj-1upln0  34461  clsk1indlem0  40759  mnuprdlem1  40995  mnuprdlem2  40996
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