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 Th7:
  (x\y)\z = (x\z)\y
proof
  (x\(x\z))\z = 0.X by Th1;
  then
A1: ((x\y)\z)\((x\y)\(x\(x\z)))=0.X by Th4;
  (x\(x\y))\y = 0.X by Th1;
  then
A2: ((x\z)\y)\((x\z)\(x\(x\y)))=0.X by Th4;
  ((x\z)\(x\(x\y)))\((x\y)\z) = 0.X by Th1;
  then
A3: ((x\z)\y)\((x\y)\z) = 0.X by A2,Th3;
  ((x\y)\(x\(x\z)))\((x\z)\y) = 0.X by Th1;
  then ((x\y)\z)\((x\z)\y) = 0.X by A1,Th3;
  hence thesis by A3,Def7;
end;
