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Theorem 0nep0 4796
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 4750 . . 3 ∅ ∈ V
21snnz 4279 . 2 {∅} ≠ ∅
32necomi 2844 1 ∅ ≠ {∅}
Colors of variables: wff setvar class
Syntax hints:  wne 2790  c0 3891  {csn 4148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-nul 4749
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ne 2791  df-v 3188  df-dif 3558  df-nul 3892  df-sn 4149
This theorem is referenced by:  0inp0  4797  opthprc  5127  2dom  7973  pw2eng  8010  hashge3el3dif  13206  isusp  21975  bj-1upln0  32641  clsk1indlem0  37818
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