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Theorem 0nep0 4372
 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 4341 . . 3
21snnz 3924 . 2
32necomi 2688 1
 Colors of variables: wff set class Syntax hints:   wne 2601  c0 3630  csn 3816 This theorem is referenced by:  0inp0  4373  opthprc  4927  2dom  7181  pw2eng  7216  isusp  18293 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-nul 4340 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 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-nul 3631  df-sn 3822
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