Eiruv Tavshilin

According to the Mishnah Brurah (O.C. 527:11), the Maharil had the practice to take the bread of his eiruv tavshilin for lechem mishnah and cut it for seudah shlishis, with the reasoning that once one mitzvah has been done with it, let him perform another mitzvah with it. When I first saw this, I wondered why specifically he should use it at seudah shlishis as opposed to at a different meal, but upon reading the Ba'er Heiteiv (p.2), I saw that he uses a slightly different wording, stating that he should take it for lechem mishnah *on the night of Shabbos* and the next day, at seudah shlishis, should cut it; this way, he has involved it in two different seudos, while only using it up during the latter. However, I wonder why the Ba'er Heiteiv only mentions the evening meal and seudah shlishis; once we're taking it out for two meals, why not take it out for all three meals?

Update, 5/22: The Be'eir Heiteiv (p. 14) and the Mishnah Brurah (p. 48) both mention this halacha a second time later in the siman, and both mention using the eiruv bread for lechem mishnah at all three meals - although I'm still not entirely clear on the B.H.'s wording in p.2. I suppose that one can extend this ruling to also use the bread as lechem mishnah on yomtov, but this is probably a very, very bad idea.