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Theorem 0inp0 4624
 Description: Something cannot be equal to both the null set and the power set of the null set. (Contributed by NM, 21-Jun-1993.)
Assertion
Ref Expression
0inp0

Proof of Theorem 0inp0
StepHypRef Expression
1 0nep0 4623 . . 3
2 neeq1 2738 . . 3
31, 2mpbiri 233 . 2
43neneqd 2659 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  =wceq 1395  =/=wne 2652   c0 3784  {csn 4029 This theorem is referenced by:  dtruALT  4684  zfpair  4689  dtruALT2  4696 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-nul 3785  df-sn 4030
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