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Theorem 0nep0 4587
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 4548 . . 3  |-  (/)  e.  _V
21snnz 4102 . 2  |-  { (/) }  =/=  (/)
32necomi 2689 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff setvar class
Syntax hints:    =/= wne 2632   (/)c0 3742   {csn 3979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441  ax-nul 4547
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-ne 2634  df-v 3058  df-dif 3418  df-nul 3743  df-sn 3980
This theorem is referenced by:  0inp0  4588  opthprc  4900  2dom  7667  pw2eng  7703  hashge3el3dif  12674  isusp  21324  bj-1upln0  31647
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