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Theorem 0nep0 4574
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 4533 . . 3  |-  (/)  e.  _V
21snnz 4104 . 2  |-  { (/) }  =/=  (/)
32necomi 2722 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff setvar class
Syntax hints:    =/= wne 2648   (/)c0 3748   {csn 3988
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-nul 4532
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-v 3080  df-dif 3442  df-nul 3749  df-sn 3989
This theorem is referenced by:  0inp0  4575  opthprc  4997  2dom  7495  pw2eng  7530  hashge3el3dif  12309  isusp  19978  bj-1upln0  32859
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