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

theorem Th4:
  for f being Morphism of E holds f is Morphism of C
proof
  let f be Morphism of E;
  f in the carrier' of E & the carrier' of E c= the carrier' of C by Th3;
  hence thesis;
end;
