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
  X is alternative & x\y=0.X implies x=y
proof
  assume that
A1: X is alternative and
A2: x\y=0.X;
  x\(x\y)=x by A2,Th2;
  then (x\x)\y=x by A1;
  then y`=x by Def5;
  hence thesis by A1,Th76;
end;
