reserve r,s,t,u for Real;

theorem
  for X being non empty TopSpace, x being Point of X, A being
a_neighborhood of x, B being Subset of X st A c= B holds B is a_neighborhood of
  x
proof
  let X be non empty TopSpace, x be Point of X, A be a_neighborhood of x, B be
  Subset of X;
  assume A c= B;
  then x in Int A & Int A c= Int B by CONNSP_2:def 1,TOPS_1:19;
  hence thesis by CONNSP_2:def 1;
end;
