Page "Gödel's ontological proof" Paragraph 69

Then, Gödel defined essences: if x is an object in some world, then the property P is said to be an essence of x if P ( x ) is true in that world and if P entails all other properties that x has in that world.

We also say that x necessarily exists if for every essence P the following is true: in every possible world, there is an element y with P ( y ).