reserve
  X for non empty set,
  FX for Filter of X,
  SFX for Subset-Family of X;

theorem
  for X be non empty set, F be Filter of X holds F <> bool X
  proof
    let X be non empty set,F be Filter of X;
    assume
A1: F = bool X;
    {} c= X;
    hence contradiction by A1,CARD_FIL:def 1;
  end;
