reserve X for BCI-algebra;
reserve x,y,z,u,a,b for Element of X;
reserve IT for non empty Subset of X;

theorem
  {0.X} is closed Ideal of X
proof
  set X1={0.X};
  reconsider X1 as Ideal of X by Lm3;
  for x being Element of X1 holds x` in X1 by Lm4;
  hence thesis by Def19;
end;
