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Theorem 0nep0 4357
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 4326 . . 3  |-  (/)  e.  _V
21snnz 3909 . 2  |-  { (/) }  =/=  (/)
32necomi 2675 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff set class
Syntax hints:    =/= wne 2593   (/)c0 3615   {csn 3801
This theorem is referenced by:  0inp0  4358  opthprc  4911  2dom  7165  pw2eng  7200  isusp  18274
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2411  ax-nul 4325
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-ne 2595  df-v 2945  df-dif 3310  df-nul 3616  df-sn 3807
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