III. Antioch as the third See in Christendom is to retain her privileges.
And so it behooves you to use the utmost vigilance, lest these depraved heretics dare to assert themselves; for you must resist them with all the authority of priests, and frequently inform us by your reports what is being done for the progress of the churches. For it is right that you should share this responsibility with the Apostolic See, and realize that the privileges of the third See in Christendom give you every confidence in action, privileges which no intrigues shall in any way impair: because my respect for the Nicene canons is such that I never have allowed nor ever will the institutions of the holy Fathers to be violated by any innovation. For different sometimes as are the deserts of individual prelates, yet the rights of their Sees are permanent: and although rivalry may perchance cause some disturbance about them, yet it cannot impair their dignity. Wherefore, brother, if ever you consider any action ought to be taken to uphold the privileges of the church of Antioch, be sure to explain it in a letter of your own, that we may be able to reply to your application completely and appropriately.
Source: Letters (New Advent)