reserve X for set;

theorem
  for A,B being Subset of X holds {A,B,{}} is N_Sub_set_fam of X
proof
  let A,B be Subset of X;
  ex F being sequence of bool X st rng F = {A,B,{}X} & F.0 = A & F.1 = B
  & for n being Element of NAT st 1 < n holds F.n = {}X by Th17;
  hence thesis by SUPINF_2:def 8;
end;
