reserve X for non empty set;

theorem
  for ET being non empty strict FMT_Space_Str st ET is Fo_filled &
  ET is U_FMT_filter holds ET is U_FMT_with_point
  proof
    let ET be non empty strict FMT_Space_Str such that
A1: ET is Fo_filled and
A2: ET is U_FMT_filter;
    for x be Element of ET holds U_FMT x is non empty by A2;
    hence thesis by A1,Th5;
  end;
