I went to remove a plastic ceiling box where a light fixture was in our home in order to install a ceiling fan brace and box, only to realize that there's actually another old popcorn ceiling above our drywall ceiling, and our ceiling drywall only seems to be supported by 2x4s, which are spaced about 2 feet apart. Is this sturdy enough to support a lightweight (< 35lb) ceiling fan, such as this one, using a simply a ceiling fan brace and box, or would something more drastic need to be done here? My question is similar to this question, except that (1) I have no attic access, as it's below our second story, and (2) the 2x4s seem to be more stable than the metal rods the new ceiling drywall was screwed to in that question.
Edit: The 2x4s appear to be around 8 feet or so long, at least. That's the width of the room, and they seem to span the width of the room, if not longer than that. On the other side I don't even seem to see if they are connected to the other side of the room.