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Theorem 0inp0 4326
 Description: Something cannot be equal to both the null set and the power set of the null set. (Contributed by NM, 30-Sep-2003.)
Assertion
Ref Expression
0inp0

Proof of Theorem 0inp0
StepHypRef Expression
1 0nep0 4325 . . 3
2 neeq1 2572 . . 3
31, 2mpbiri 225 . 2
43neneqd 2580 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1649   wne 2564  c0 3585  csn 3771 This theorem is referenced by:  dtruALT  4351  zfpair  4356  dtruALT2  4363 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382  ax-nul 4293 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-ne 2566  df-v 2915  df-dif 3280  df-nul 3586  df-sn 3777
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