
theorem Th9:
  for C being non empty composable with_identities CategoryStr,
      f1,f2 being morphism of C st f1 = cod f2 holds f1 |> f2 & f1 (*) f2 = f2
  proof
    let C be non empty composable with_identities CategoryStr;
    let f1,f2 be morphism of C;
    assume f1 = cod f2;
    then consider f be morphism of C such that
A1: f1 = f & f |> f2 & f is identity by CAT_6:def 19;
    thus f1 |> f2 by A1;
    thus f1 (*) f2 = f2 by A1,CAT_6:def 4,def 14;
  end;
