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 p-Semisimple iff for x,y,z holds x\(y\z)=(z\y)\x`
proof
  thus X is p-Semisimple implies for x,y,z holds x\(y\z)=(z\y)\x` by Lm13;
  assume
A1: for x,y,z holds x\(y\z)=(z\y)\x`;
  for x,y holds x\y`=y\x`
  proof
    let x,y;
    x\y`=(y\0.X)\x` by A1;
    hence thesis by Th2;
  end;
  hence thesis by Th63;
end;
