This is part of the letter to Bishop Antonius [1272], in which Cyprian explains the validity of the election of Cornelius against his detractors, especially Novatian, who was ordained bishop against Cornelius.
The passage does not state explicitly what ecclesiastical grades Cornelius really followed. Actually, he may have been only a deacon before his episcopal election, but the wording of Cyprian ("omnia ecclesiastica officia") in reality suggests all grades, including that of deacon and presbyter. Incidentally, the description of the ecclesiastical career of Cornelius shows how different it was from that of Cyprian himself.