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Theorem 0nep0 5028
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 4984 . . 3 ∅ ∈ V
21snnz 4499 . 2 {∅} ≠ ∅
32necomi 3032 1 ∅ ≠ {∅}
Colors of variables: wff setvar class
Syntax hints:  wne 2978  c0 4116  {csn 4370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-ext 2784  ax-nul 4983
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-nfc 2937  df-ne 2979  df-v 3393  df-dif 3772  df-nul 4117  df-sn 4371
This theorem is referenced by:  0inp0  5029  opthprc  5367  2dom  8261  pw2eng  8301  hashge3el3dif  13481  isusp  22274  bj-1upln0  33302  clsk1indlem0  38833
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