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Theorem 0nep0 4260
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 4229 . . 3  |-  (/)  e.  _V
21snnz 3820 . 2  |-  { (/) }  =/=  (/)
32necomi 2603 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff set class
Syntax hints:    =/= wne 2521   (/)c0 3531   {csn 3716
This theorem is referenced by:  0inp0  4261  opthprc  4815  2dom  7018  pw2eng  7053  isusp  23560
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339  ax-nul 4228
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ne 2523  df-v 2866  df-dif 3231  df-nul 3532  df-sn 3722
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