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

theorem Th10:
  for L being satisfying_DN_1 non empty ComplLLattStr, x, y, z
  being Element of L holds (x + ((y + z)` + (y + x)`)`)` = (y + x)`
proof
  let L be satisfying_DN_1 non empty ComplLLattStr;
  let x, y, z be Element of L;
  set Z = (y + x)`, X = (y + z)`, Y = x;
  (((X + Y)` + Z)` + (X + Z)`)` = Z by Th9;
  hence thesis by Th9;
end;
