
theorem Th3:
  for C being composable CategoryStr, f1,f2,f3 being morphism of C st
  f1 |> f2 & f2 |> f3 & f2 is identity holds f1 |> f3
  proof
    let C be composable CategoryStr;
    let f1,f2,f3 be morphism of C;
A1: C is right_composable by CAT_6:def 11;
    assume
A2: f1 |> f2 & f2 |> f3;
    assume f2 is identity;
    then f2(*)f3 = f3 by A2,CAT_6:def 14,def 4;
    hence f1 |> f3 by A2,A1,CAT_6:def 9;
  end;
