If it is said:
“You have assumed the absence of necessary existence. How, then, can it exist under the assumption of its nonexistence, on the basis of the proof you have presented?”

We reply:
An impossible assumption may entail something that exists, whether necessarily or contingently, just as it may entail something impossible. An assumption is a condition that entails its consequent. The realization of the antecedent entails the realization of the consequent, but its absence does not entail the absence of the consequent.

This is like saying:
“If it were possible for two contraries to occur together, this would require an originator.” Indeed, the consequent may hold under either of two contradictory assumptions, as with the existence of the Creator in relation to each created thing: He exists whether that thing exists or not.

Thus, an impossible assumption—namely, the assumption that the Necessary Existent does not exist—may entail His existence, just as a possible assumption may do so. If His nonexistence is assumed, the objection mentioned above must be invalid. This entails that the proof stands free of the opposing argument, and the proof entails His existence.

Furthermore, the assumption of His nonexistence is in fact impossible, and an impossible assumption may entail something impossible. Thus, the assumption of His nonexistence entails the conjunction of two contradictories: the affirmation of His existence together with the affirmation of His nonexistence. This is impossible. It is therefore known that the assumption of His nonexistence is impossible, which is what was to be established, and that He must exist—even if His nonexistence is supposed in the mind. Supposing His nonexistence in the mind does not contradict His existence in external reality. His existence has been established, so He must exist under every assumption. This and other considerations make clear