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Theorem 0nep0 4405
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 4370 . . 3  |-  (/)  e.  _V
21snnz 3951 . 2  |-  { (/) }  =/=  (/)
32necomi 2693 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff set class
Syntax hints:    =/= wne 2606   (/)c0 3616   {csn 3843
This theorem is referenced by:  0inp0  4406  opthprc  4960  2dom  7215  pw2eng  7250  isusp  18329
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-nul 4369
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-v 2967  df-dif 3312  df-nul 3617  df-sn 3849
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