reserve A, B for non empty set,
  A1, A2, A3 for non empty Subset of A;
reserve X for TopSpace;
reserve X for non empty TopSpace;
reserve X1, X2 for non empty SubSpace of X;

theorem Th10:
  X1 is SubSpace of X2 implies for x1 being Point of X1
  ex x2 being Point of X2 st x2 = x1
proof
  assume X1 is SubSpace of X2;
  then
A1: the carrier of X1 c= the carrier of X2 by TSEP_1:4;
  let x1 be Point of X1;
  x1 in the carrier of X1;
  then reconsider x2 = x1 as Point of X2 by A1;
  take x2;
  thus thesis;
end;
