reserve X for BCI-algebra;
reserve X1 for non empty Subset of X;
reserve A,I for Ideal of X;
reserve x,y,z for Element of X;
reserve a for Element of A;
reserve X for BCK-algebra;
reserve X for BCI-algebra;
reserve X for BCK-algebra;
reserve I for Ideal of X;
reserve I for Ideal of X;

theorem
  (for I being Ideal of X holds I is commutative Ideal of X) iff for x,y
  being Element of X st x<= y holds x= y\(y\x)
by BCIALG_3:5,Th37;
