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
  union {} = {}
proof
  now
    given x such that
A1: x in union {};
    ex X being set st x in X & X in {} by A1,TARSKI:def 4;
    hence contradiction;
  end;
  hence thesis by XBOOLE_0:7;
end;
