reserve L for satisfying_DN_1 non empty ComplLLattStr;
reserve x, y, z for Element of L;

theorem Th47:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (((x + y)` + z)` + (x` + y)`)` + y = (x` + y)``
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  ((((x + y)` + z)` + (x` + y)`)` + y)`` = (x` + y)`` by Th11;
  hence thesis by Th23;
end;
