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
  for X being BCI-Algebra_with_Condition(S) holds for x being Element of
  X holds x |^ 3 = x * x * x
proof
  let X be BCI-Algebra_with_Condition(S);
  let x be Element of X;
  thus x|^3 = x|^(2 + 1) .=(x|^2) * x by Def6
    .= x * x * x by Th22;
end;
