reserve X for non empty TopSpace;
reserve x for Point of X;
reserve U1 for Subset of X;

theorem Th4:
  for U1 being Subset of X, x being Point of X st U1 is
  a_neighborhood of x holds x in U1
proof
  let U1 be Subset of X, x be Point of X;
  assume U1 is a_neighborhood of x;
  then
A1: x in Int (U1) by Def1;
  Int(U1) c= U1 by TOPS_1:16;
  hence thesis by A1;
end;
