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
  the carrier of X is closed Ideal of X
proof
A1: ( for x being Element of X holds x` in the carrier of X)& for x,y being
Element of X st x\y in the carrier of X & y in the carrier of X
  holds x in the carrier of X;
  the carrier of X is non empty Subset of X & 0.X in the carrier of X by
ZFMISC_1:def 1;
  hence thesis by A1,Def18,Def19;
end;
