reserve T for non empty TopSpace,
  A, B for Subset of T,
  F, G for Subset-Family of T,
  x for set;

theorem Th28:
  for T being non empty TopSpace, A being Subset of T holds Der A c= Cl A
proof
  let T be non empty TopSpace, A be Subset of T;
  let x be object;
  assume
A1: x in Der A;
  then reconsider x9 = x as Point of T;
  for G being Subset of T st G is open holds x9 in G implies A meets G
  proof
    let G be Subset of T;
    assume
A2: G is open;
    assume x9 in G;
    then ex y being Point of T st y in A /\ G & x <> y by A1,A2,Th17;
    hence thesis;
  end;
  hence thesis by PRE_TOPC:24;
end;
