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Theorem notm0 3389
 Description: A class is not inhabited if and only if it is empty. (Contributed by Jim Kingdon, 1-Jul-2022.)
Assertion
Ref Expression
notm0
Distinct variable group:   ,

Proof of Theorem notm0
StepHypRef Expression
1 eq0 3387 . 2
2 alnex 1476 . 2
31, 2bitr2i 184 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104  wal 1330   wceq 1332  wex 1469   wcel 1481  c0 3369 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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-dif 3079  df-nul 3370 This theorem is referenced by:  disjnim  3929  pwntru  4131  exmidn0m  4133  mapprc  6555  map0g  6591  ixpprc  6622  ixp0  6634  exmidfodomrlemim  7077  ntreq0  12360  blssioo  12773  pwtrufal  13384
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