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} implies x = y
proof
  assume {x} /\ {y} = {x};
  then x in {y} or y in {x} by Lm7;
  hence thesis by TARSKI:def 1;
end;
