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

theorem Th47:
  X \ X /\ Y = X \ Y
proof
  now
    let x be object;
    x in X & not x in X /\ Y iff x in X & not x in Y by XBOOLE_0:def 4;
    hence x in X \ X /\ Y iff x in X \ Y by XBOOLE_0:def 5;
  end;
  hence thesis by TARSKI:2;
end;
