procedure TForm1.Button1Click(Sender: TObject);
var
  sl: TStringList;
begin
  sl := TStringList.Create;
  try
    with sl do
    begin
      Sorted := True;
      Duplicates := dupIgnore;
      Add(Edit1.Text);
    end;
    Listbox1.Items.Assign(sl);
  finally
    sl.Free;
  end;
end; 