reserve x,y,X for set;

theorem Th2:
  for T being non empty TopSpace, x being Point of T, A being set
  holds A in NeighborhoodSystem x iff A is a_neighborhood of x
proof
  let T be non empty TopSpace, x be Point of T, B be set;
  B in NeighborhoodSystem x iff ex A being a_neighborhood of x st B = A;
  hence thesis;
end;
