 We can express (EDR) in a more compact manner by resorting to further formalization (the following notation is used, e.g., in Correia 2008). We can use the sentential operator “\(\square\)” for metaphysical necessity, the one-place predicate “E” for existence, and the two-place sentential operator “→” for material implication. Following this notation, we can formalize rigid existential dependence as follows: “\(\square(Ex \rightarrow Ey)\)”, which can be read as “x rigidly depends for its existence on y”, or alternatively “x rigidly necessitates y”. Note that (EDR), somewhat controversially, implies that everything dependsR for its existence upon itself. It would, of course, be easy enough to modify (EDR)’s definiens to read “y is not identical with x and, necessarily, x exists only if y exists”, but that would have the disadvantage of precluding anything from dependingR for its existence upon itself.