Papal Infallibility Ex Cathedra
Dogmatic Constitution "Pastor Aeternus"
Romanum pontificem, cum ex cathedra loquitur, id est, cum omnium christianorum pastoris et doctoris munere fungens, pro suprema sua apostolica auctoritate doctrinam de fide vel moribus ab universa ecclesia tenendam definit, per assistentiam divinam, ipsi in beato Petro promissam, ea infallibilitate pollere, qua divinus Redemptor ecclesiam suam in definienda doctrina de fide vel moribus instructam esse voluit;
ideoque eiusmodi Romani pontificis definitiones ex sese, non autem ex consensu ecclesiae irreformabiles esse.
illustrating mediæval and modern history
We teach and define that it is a dogma Divinely revealed that the Roman pontiff when he speaks ex cathedra, that is when in discharge of the office of pastor and doctor of all Christians, by virtue of his supreme Apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the Divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the Divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals, and that therefore such definitions of the Roman pontiff are of themselves and not from the consent of the Church irreformable.
Papal encyclical "Humani Generis"
20. Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent, since in writing such Letters the Popes do not exercise the supreme power of their Teaching Authority. For these matters are taught with the ordinary teaching authority, of which it is true to say:
"He who heareth you, heareth me"