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Theorem 0nep0 4143
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 4108 . . 3  |-  (/)  e.  _V
21snnz 3694 . 2  |-  { (/) }  =/=  (/)
32necomi 2420 1  |-  (/)  =/=  { (/)
}
Colors of variables: wff set class
Syntax hints:    =/= wne 2335   (/)c0 3408   {csn 3575
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147  ax-nul 4107
This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2296  df-ne 2336  df-v 2727  df-dif 3117  df-nul 3409  df-sn 3581
This theorem is referenced by:  0inp0  4144  opthprc  4654  2dom  6767  exmidpw  6870  exmidaclem  7160  pw1dom2  7179
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