
theorem Th21:
  for X, Y being TopSpace, XV being SubSpace of X, YV being
  SubSpace of Y holds [:XV, YV:] is SubSpace of [:X, Y:]
proof
  let X, Y be TopSpace, XV be SubSpace of X, YV be SubSpace of Y;
  [:XV, Y:] is SubSpace of [:X, Y:] & [:XV, YV:] is SubSpace of [:XV, Y:]
  by Lm6,Th15;
  hence thesis by TSEP_1:7;
end;
