reserve X,Y,Z,X1,X2,Y1,Y2 for set, x,y,z,t,x1,x2 for object,
  f,g,h,f1,f2,g1,g2 for Function;

theorem Th1:
  ~{} = {}
proof
  [:{} qua set,{}:] = {} & dom {} = {} by ZFMISC_1:90;
  then dom ~{} = {} by FUNCT_4:46;
  hence thesis;
