We are informed by the texts of the gospels that in this Church and in its power are two swords; namely, the spiritual and the temporal”
The swords being referred to are a customary reference to the swords yielded by the Apostles upon Christ's arrest, which were said to have been buried next to the Apostle Peter. Early theologians believed that if there are two swords one must be subordinate to the other. It then became a spiritual hierarchal ladder, the spiritual judges the secular "on account of its greatness and sublimity, while the lower spiritual power is judged by the higher spiritual power, etc. Thus, it was concluded, the temporal authorities must submit to the spiritual authorities, not merely on matters concerning doctrine and morality: "For with truth as our witness, it belongs to spiritual power to establish the terrestrial power and to pass judgment if it has not been good."
The Bull ends with:
“Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.]"