reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem Th10:
  for a being Object of E holds (Obj incl E).a = a
proof
  let a be Object of E;
  reconsider a9 = a as Object of C by Th2;
  id a9 = id a by Def4
    .= (incl E).(id a) by FUNCT_1:18
    .= id((Obj incl E).a) by CAT_1:68;
  hence thesis by CAT_1:59;
end;
