MySQL Sub search - Is there such a thing?

Some one is asking me to create a sub search on a search that has already been done. For instance, the database has 50,000 records, a user does a search for two keywords which yielded 1700 records. They want to now filter that list with other keywords. The logic is that searching 1700 records has got to be faster than searching 50,000 records. The only way I know how to do this is to save the results of the pervious search to hidden fields and allow the user to add more keywords, which in essence isn't doing other than adding more keywords to the search doing the same exact thing they did before with new keywords. Is this logic correct or is there a way to save that queries results and search only that? Thanks