reserve C for CategoryStr;
reserve f,f1,f2,f3 for morphism of C;
reserve g1,g2 for morphism of C opp;

theorem Th26:
  for C being composable with_identities CategoryStr, f,f1 being morphism of C
  st f |> f1 & f1 is identity holds dom f = f1
  proof
    let C be composable with_identities CategoryStr;
    let f,f1 be morphism of C;
    assume
A1: f |> f1 & f1 is identity;
    then
A2: C is non empty;
    then reconsider o = f1 as Object of C by A1,Th22;
    ex f11 being morphism of C st o = f11 & f |> f11 & f11 is identity by A1;
    hence dom f = f1 by A2,Def18;
  end;
