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Theorem 0nep0 5358
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 5307 . . 3 ∅ ∈ V
21snnz 4776 . 2 {∅} ≠ ∅
32necomi 2995 1 ∅ ≠ {∅}
Colors of variables: wff setvar class
Syntax hints:  wne 2940  c0 4333  {csn 4626
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-nul 5306
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-v 3482  df-dif 3954  df-nul 4334  df-sn 4627
This theorem is referenced by:  0inp0  5359  opthprc  5749  2dom  9070  pw2eng  9118  djuexb  9949  hashge3el3dif  14526  cat1  18142  isusp  24270  bj-1upln0  37010  clsk1indlem0  44054  mnuprdlem1  44291  mnuprdlem2  44292
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