Full Idea
The objects upon which a given object depends, according to the present account, are those which must figure in any of the logically equivalent definitions of the object. They will, in a sense, be ineliminable.
Gist of Idea
An object depends on another if the second cannot be eliminated from the first's definition
Source
Kit Fine (Ontological Dependence [1995], II)
Book Reference
-: 'Aristotelian Society' [], p.279
A Reaction
This is Fine's main proposal for the dependency relationship, with a context of Aristotelian essences understood as definitions. Sounds pretty good to me.