[Nagata embedding][1] is another black box - its statement is very simple and useful, but its proof is hard.

By combining Nagata embedding with Hironaka's resolution of singularities (mentioned in another answer), you get "any smooth variety over a characteristic zero field admits an open immersion into a proper smooth variety", which is concise enough that people often use it without citing the authors' hard work.


  [1]: http://arxiv.org/abs/0706.1907