reserve C for Category,
  C1,C2 for Subcategory of C;

theorem
  for C,D being Category, F being Functor of C,D holds
  F is Functor of C, Image F
proof
  let C,D be Category, F be Functor of C,D;
  rng F c= the carrier' of Image F by Def3;
  hence thesis by Th7;
end;
