reserve e,u for set;
reserve X, Y for non empty TopSpace;

theorem Th9:
  for A being Subset of X, B being Subset of Y, V being
  a_neighborhood of A, W being a_neighborhood of B holds [:V,W:] is
  a_neighborhood of [:A,B:]
proof
  let A be Subset of X, B be Subset of Y, V be a_neighborhood of A, W be
  a_neighborhood of B;
  A c= Int V & B c= Int W by CONNSP_2:def 2;
  then [:A,B:] c= [:Int V, Int W:] by ZFMISC_1:96;
  hence [:A,B:] c= Int [:V,W:] by Th7;
end;
