I guess the first thing I should do is to establish what exactly is meant by `dependency’. If X is dependent on Y then Y is a cause of X’s existence. If X is dependent only on Y then Y is the cause of X’s existence, otherwise the cause of X’s existence is the sum of all the things on which it’s existence depends. I think it is clear that a depended upon thing must exist prior to that which depends upon it and this rules out the option of a thing depending upon only itself for its existence. This leaves only two valid options, if something exists then either it is dependent on something apart from itself for it’s existence or else it is dependent on nothing for it’s existence.
This, I think, establishes the first premise.