The way I've read it, many fundamental facts about Grothendieck categories, such as completeness, are special cases of those about locally presentable categories (see, for example, this answer).
However, it doesn't seem that obvious that Grothendieck categories are locally presentable. Is there a reference proving that? Wikipedia page on Grothendieck categories says that it is a consequence of Gabriel-Popescu theorem. Surely, there must be an easier way to show that?