vesa'adu libechem - and you will refresh your hearts
These words are clear proof that Avraham had realized already that the men he was facing were angels though they appeared to him in the guise of ordinary mortals. This is why he spoke of libechem when he referred to their heart. Had they been human beings Avraham should have said levav as we know from Tehillim 104:15 "velechem levav-enosh yisad - and bread refreshes the heart of man." Angels who do not have an evil urge (yetzer hara) (Megillah 14) have a heart which is simple, not exposed to contradictory demands by two urges, the yetzer tov (good urge) and the yetzer ra.
The absence of a letter such as this vet has often been the means by which we have learned a variety of lessons. For instance, in Shemot 31:17 the Torah writes "ki sheshet yamim asah Hashem et-hashamayim ve'et-ha'aretz - for in six days G-d completed the making of the heaven and earth." According to correct grammar, the word sheshet should have been preceded by the letter bet for this translation to be correct. The absence of that letter teaches that the maximum period of time which this universe is going to endure before undergoing a major transformation is six thousand years, seeing that in G-d's calendar one thousand years in our time are only considered one day. (Bereishit Rabbah 19:14 based on Tehillim 90:4)
This is another example teaching that not a single letter in the Torah, be it a letter too many or a letter too few, is without profound significance. Moshe stressed this point when near the end of his life (Devarim 32:47) he said, "for not a single word is empty, [devoid of meaning] for you."