reserve X for BCK-algebra;
reserve x,y for Element of X;
reserve IT for non empty Subset of X;

theorem
  IT is Commutative-Ideal of X implies for x,y being Element of X st x\y
  in IT holds x\(y\(y\x)) in IT
proof
  assume
A1: IT is Commutative-Ideal of X;
  let x,y be Element of X;
  assume x\y in IT;
  then
A2: (x\y)\0.X in IT by BCIALG_1:2;
  thus thesis by A1,A2,Def10;
end;
