
theorem Th7:
  for C being composable with_identities CategoryStr,
      f1,f2 being morphism of C st f1 |> f2 & f1 is identity & f2 is identity
  holds f1 = f2
  proof
    let C be composable with_identities CategoryStr;
    let f1,f2 be morphism of C;
    assume
A1: f1 |> f2;
    assume
A2: f1 is identity;
    assume f2 is identity;
    hence f1 = f1 (*) f2 by A1,CAT_6:def 5,def 14
    .= f2 by A1,A2,CAT_6:def 4,def 14;
  end;
