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Theorem 0nep0 4089
 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 4055 . . 3
21snnz 3642 . 2
32necomi 2393 1
 Colors of variables: wff set class Syntax hints:   wne 2308  c0 3363  csn 3527 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 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-nul 4054 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-v 2688  df-dif 3073  df-nul 3364  df-sn 3533 This theorem is referenced by:  0inp0  4090  opthprc  4590  2dom  6699  exmidpw  6802  exmidaclem  7064  pw1dom2  13190
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