The category being separated is "disciplines", which divides into "BS" and "non-BS". "Academic" disciplines are thus a further subcategory of "BS" disciplines.

Actually, "academic" disciplines would probably be a subcategory of "disciplines" which is largely but not entirely subsumed by "BS" disciplines, but I don't usually demand that level of precision from witticisms.

[For the record, separating a category into two subcategories and proving one of them empty is just another way of proving the original category is identical with the non-empty subcategory. It is, indeed, valid from a technical perspective.]