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
  {0.X} 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,Th36;
