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 Th21:
  for X being BCI-Algebra_with_Condition(S) holds for x being
  Element of X holds x |^ 1 = x
proof
  let X be BCI-Algebra_with_Condition(S);
  let x be Element of X;
  thus x|^1 = x|^(0 + 1) .=(x|^0) * x by Def6
    .=0.X * x by Def6
    .= x by Th8;
end;
