theorem
  {x,y} /\ X = {x,y} implies x in X
proof
  assume {x,y} /\ X = {x,y};
  then x in {x,y} /\ X & y in {x,y} /\ X or x in X /\ {x,y} & y in X /\ {x,y}
  by TARSKI:def 2;
  hence thesis by XBOOLE_0:def 4;
end;
