The first is false, the second is irrelevant.
RE: The first is false, the second is irrelevant.
I agree with you on both.
But the second one is self-referential. It sounds like, I proclaim that I am infallible, therefore I am.
Actually the first, and all such ex-cathedra statements, depends upon the second. For as said. Rome has presumed to infallibly declare she is and will be perpetually infallible whenever she speaks in accordance with her infallibly defined (scope and subject-based) formula, which renders her declaration that she is infallible, to be infallible, as well as all else she accordingly declares.
Thus we have such bombast as this:
"It was the charge of the Reformers that the Catholic doctrines were not primitive, and their pretension was to revert to antiquity. But the appeal to antiquity is both a treason and a heresy. It is a treason because it rejects the Divine voice of the Church at this hour, and a heresy because it denies that voice to be Divine." "I may say in strict truth that the Church has no antiquity. It rests upon its own supernatural and perpetual consciousness. Its past is present with it, for both are one to a mind which is immutable. Primitive and modern are predicates, not of truth, but of ourselves." "The only Divine evidence to us of what was primitive is the witness and voice of the Church at this hour." — Most Rev. Dr. Henry Edward Cardinal Manning, Lord Archbishop of Westminster, “The Temporal Mission of the Holy Ghost: Or Reason and Revelation,” (New York: J.P. Kenedy & Sons, originally written 1865, reprinted with no date), pp. 227-228.