reserve A,B,C for Category,
  F,F1 for Functor of A,B;

theorem Th4:
  for f being Morphism of A holds f(*)(id dom f) = f
proof
  let f be Morphism of A;
  reconsider f9 = f as Morphism of dom f, cod f by CAT_1:4;
A1: Hom(dom f, cod f) <> {} by CAT_1:2;
  Hom(dom f,dom f) <> {};
  hence f(*)(id dom f) = f9*(id dom f) by A1,CAT_1:def 13
    .= f by A1,CAT_1:29;
end;
