reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;

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;
