All nouns are exclipsed when following preposition + article.
Le fear = with a man; leis an bhfear = with the man.
Excluding the combined preposition + article forms den, don, sa, and san ; excluding the article na following a preposition; and excluding nouns beginning with D, T, or a vowel (except for the phrase um an dtaca, which does eclipse taca ).
EDIT: In the 2016 Caighdeán, either (den and don) or (sa) can also eclipse.
As @LauraDoherty said,
\Have a look at this discussion, it explains it.
Basically, "le = with" whilst "le + an -> leis an = with the".
Why is there no "n" pronounced in "an bhfear" ? It kind if sounds like 'leis (eh) bhfear'
That's just the way it is: the "-n" of "an" is dropped in running speech (except before a vowel). I remember it being one of the first things a "mother-tongue" speaker of Irish pointed out to me when I was learning Irish the first time around. (That was nearly 50 years ago, so I've had plenty of time to forget nearly all of it; which is why I'm beginning again now with duolingo!)
Regarding the pronunciation of "bhfear". I thought when the f was eclipsed by the bh it made a "w" sound- is that only for broad vowels? And a "v" sound for slender vowels?