any friend of _________s is a friend of mine.

Any friend of _________s is a friend of mine is often spoken in reference to a friend of a friend. When someone says if youre a friend of theirs, youre a friend of mine, they are saying that if your mutual friend thinks highly of you, then you must be good and trustworthy and therefore could also be a good friend. It is often spoken about a friend of a friend or a mutual friend of yours, someone you dont know well but will trust due to this mutual friendship.