reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem Th39:
  X \/ (Y \ X) = X \/ Y
proof
  thus X \/ (Y \ X) c= X \/ Y
  proof
    let x be object;
    assume x in X \/ (Y \ X);
    then x in X or x in Y \ X by XBOOLE_0:def 3;
    then x in X or x in Y by XBOOLE_0:def 5;
    hence thesis by XBOOLE_0:def 3;
  end;
  let x be object;
  assume x in X \/ Y;
  then x in X or x in Y & not x in X by XBOOLE_0:def 3;
  then x in X or x in Y \ X by XBOOLE_0:def 5;
  hence thesis by XBOOLE_0:def 3;
end;
