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 Th10:
  for X being BCI-Algebra_with_Condition(S) holds for x,y,z being
  Element of X holds (x*y)*z = (x*z)*y
proof
  let X be BCI-Algebra_with_Condition(S);
  let x,y,z be Element of X;
  (x*y)*z = x*(y*z) by Th9
    .= (y*z)*x by Th6
    .= y*(z*x) by Th9
    .= (z*x)*y by Th6;
  hence thesis by Th6;
end;
