reserve X for non empty BCIStr_1;
reserve d for Element of X;
reserve n,m,k for Nat;
reserve f for sequence of  the carrier of X;

theorem Th16:
  for X being BCI-Algebra_with_Condition(S) holds 0.X
  is_a_unity_wrt the ExternalDiff of X
proof
  let X be BCI-Algebra_with_Condition(S);
  now
    let a be Element of X;
    thus (the ExternalDiff of X).(0.X,a) = 0.X * a .= a by Th8;
    thus (the ExternalDiff of X).(a,0.X) = a * 0.X .= a by Th8;
  end;
  hence thesis by BINOP_1:3;
end;
