[quote=First Vatican Council]5. The Roman pontiffs, too, as the circumstances of the time or the state of affairs suggested, sometimes by summoning ecumenical councils or consulting the opinion of the Churches scattered throughout the world, sometimes by special synods, sometimes by taking advantage of other useful means afforded by divine providence, defined as doctrines to be held those things which, by God’s help, they knew to be in keeping with Sacred Scripture and the apostolic traditions.
6. For the Holy Spirit was promised to the successors of Peter not so that they might, by his revelation, make known some new doctrine, but that, by his assistance, they might religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles.
Indeed, their apostolic teaching was embraced by all the venerable fathers and reverenced and followed by all the holy orthodox doctors, for they knew very well that this See of St. Peter always remains unblemished by any error, in accordance with the divine promise of our Lord and Savior to the prince of his disciples: I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren .
7. This gift of truth and never-failing faith was therefore divinely conferred on Peter and his successors in this See so that they might discharge their exalted office for the salvation of all, and so that the whole flock of Christ might be kept away by them from the poisonous food of error and be nourished with the sustenance of heavenly doctrine. Thus the tendency to schism is removed and the whole Church is preserved in unity, and, resting on its foundation, can stand firm against the gates of hell.
8. But since in this very age when the salutary effectiveness of the apostolic office is most especially needed, not a few are to be found who disparage its authority, we judge it absolutely necessary to affirm solemnly the prerogative which the only-begotten Son of God was pleased to attach to the supreme pastoral office.
9. Therefore, faithfully adhering to the tradition received from the beginning of the Christian faith, to the glory of God our savior, for the exaltation of the Catholic religion and for the salvation of the Christian people, with the approval of the Sacred Council, we teach and define as a divinely revealed dogma that when the Roman Pontiff speaks EX CATHEDRA, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable.
So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema.
Feel free to PM me with questions OP.