Out of Sight, Out of Mind

(Grammar Questions I Couldn't Answer)

This is another question I created for myself.

Since I started doing the proverbs lessons, I've committed myself to pulling apart and dissecting all the grammar of common English proverbs.  (As inspired by Scott Thornbury's example in Beyond the Sentence).

But in committing myself to this project, I sometimes find myself ending up with proverbs I don't know how to analyze.

For example: "Out of sight, out of mind" ----Slideshow (slides, pub), Worksheet (docs, pub),

"sight" and "mind" are simple enough.  (They're both nouns).  But how to classify "out" and "of" .  Is "of" a preposition modifying "out" ?
I've consulted some dictionaries that say "out of" is to be regarded as just one word, and it functions as a preposition.

So "out of sight" is a prepositional phrase then?  "Out of" is the preposition, and "sight" is the object of the preposition?  But then what is the prepositional phrase modifying?

I took a stab at reconstructing the full sentence, and my guess: "If something is out of sight, then it is also out of mind".  Is this correct?