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

theorem Th3:
  for f being Morphism of A holds (id cod f)(*)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(cod f,cod f) <> {};
  hence (id cod f)(*)f = (id cod f)*f9 by A1,CAT_1:def 13
    .= f by A1,CAT_1:28;
end;
