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“...How could a true Pope be elected when there are no true Cardinals left alive to elect him?”

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Actually, the First Vatican Council does not teach that there will always be a Pope. The council could not possibly teach such a thing because this is obviously false, since there is always a period of no Pope (a so-called “interregnum”) after one Pope dies and before a new one is elected, and in Church history this period has sometimes lasted even for years. What Vatican I truly teaches is this: “Therefore, if anyone says that it is not by the institution of Christ the lord himself (that is to say, by divine law) that blessed Peter should have perpetual successors in the primacy over the whole church; or that the Roman pontiff is not the successor of blessed Peter in this primacy: let him be anathema” (Dogmatic Constitution Pastor Aeternus). The key phrase is “in the primacy”. The council is teaching that the primacy that was conferred upon St. Peter is retained in all his valid successors perpetually. In other words, for as long as there is a valid Pope, this Pope will enjoy the same primacy that St. Peter had received from our Lord — there will never be a Pope who will be a successor to St. Peter but not also have the same primacy, and this is guaranteed in perpetuity. That is what the council is teaching; it has nothing to do with how long of an interregnum the Church can endure. We explain this in greater detail in this post.

As far as the accusation that Sedevacantism would mean that the gates of hell have prevailed against the Church, which Christ our Lord promised would never happen (see Mt 16:18), nothing could be further from the truth. In fact, the opposite is true: Only if the Vatican II “popes” are invalid can we affirm that the gates of hell have not prevailed. This is easy to see once we understand what the Church teaches is meant by the gates of hell prevailing. We have put all the evidence together in this detailed article, and we also have a brief video that explains the essentials.

From https://novusordowatch.org/faqs/

(Question 8)