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 Th56:
  X is p-Semisimple iff for x,y,z holds (z\y)\(z\x) = x\y
proof
  X is p-Semisimple iff for x,y holds y\(y\x) = x;
  hence thesis by Lm8;
end;
