reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  ex C being U-petit Category st
  not the carrier of C is Element of U & not the carrier' of C is Element of U
  proof
    consider o be set such that
A1: not o in U by CLASSES4:83;
    set C = 1Cat(o, o);
    now
      thus C is U-petit by Th61;
      C = CatStr(# { o },{ o},  o:-> o,o:->o,(o,o):->o #) by CAT_1:def 11;
      hence not the carrier of C is Element of U &
        not the carrier' of C is Element of U by A1,Th18;
    end;
    hence thesis;
  end;
