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;

theorem
  {0.X} is commutative Ideal of X iff for I being Ideal of X holds I is
  commutative Ideal of X
by Th37,Th36;
