God’s necessary existence, the even weaker principle of sufficient reason and origin essentialism

Let God be defined as personal first cause. The even weaker principle of sufficient reason merely asserts that the existence of all actual beings is explainable. That is to say, for each being in the actual world there is a possible world in which that being exists and is explained. In what follows I show that (i) if God exists and (ii) if the even weaker principle of sufficient reason holds, God exists necessarily.

Suppose God exists. So God exists in the actual world. Consider a possible world in which the being referred to as 'God' in the actual world exists and is explained. Since it's God and thus uncaused in the actual world, it's also uncaused in the possible world in which its existence is explained. Therefore this explanation cannot be a causal explanation. But then the only explanatory option left is a sound ontological argument for its existence. This being thus exists necessarily. Hence God exists necessarily.

My argument actually needs origin essentialism as an additional premise. For the claim that the being referred to as ‘God’ in the actual world is also uncaused in the possible world in which it exists and is explained, follows if we accept the further premise that beings have their causes essentially. That is to say, if a being is caused in some possible world, then it has that cause in all possible worlds in which it exists.

Indeed, suppose for reductio ad absurdum that the being referred to as 'God' in the actual world is caused in the possible world in which it exists and is explainded. Since on origin essentialism this being has that cause essentially, it also has that cause in the actual world. But the being is uncaused in the actual world. After all, it's God in the actual world. We thus arrive at a contradiction. Hence the being is not caused in the possible world in which it is explained.