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Theorem 0nep0 4197
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 4166 . . 3  |-  (/)  e.  _V
21snnz 3757 . 2  |-  { (/) }  =/=  (/)
32necomi 2541 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff set class
Syntax hints:    =/= wne 2459   (/)c0 3468   {csn 3653
This theorem is referenced by:  0inp0  4198  opthprc  4752  2dom  6949  pw2eng  6984
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-nul 4165
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-v 2803  df-dif 3168  df-nul 3469  df-sn 3659
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