From my midterm in Early Christian Writings, taken last Thursday (paragraph numbering not in original):
1. Ecclesiology means the study of the Church. Early Christians had to determine the structure or hierarchy of the Church, and how and to whom membership in her was given. St. Paul’s “First Letter to the Corinthians” and the anonymous Didache state that the Church hierarchy is made of prophets, Apostles, and teachers. They warn against false prophets; the Didache gives ways to discern a false prophet (e.g., he stays in one town for more than two days or asks for money). Tertullian said, in his Prescription Against Heretics, that the Rule of Faith (teaching of Christ handed down through the Apostles and their successors) is the measuring stick of orthodoxy, and that Gnostic heretics were not a part of the Church (which St. Paul calls the one mystical body of Christ in his aforementioned letter).
2. St. Ignatius the God-bearing martyr and bishop of Antioch taught the trifold ministry of deacons, priests, and bishops (ascending order of rank) in his ca. 110 “Letter to the Trallians.” This has been the model of the Church ever since.
3. St. Paul taught, in the letter cited, that people enter into the Church by baptism. What about people who were baptized by heretics? St. Cyprian, the martyred bishop of Carthage, thought of the Church as a tree with a trunk of common belief (or a trunk of the throne of St. Peter, the See of Rome, in a later version) and many branches (sees/bishoprics) in his treatise On the Unity of the Church. He very clearly taught that there is no salvation outside the Church, and that heretics belong to the lifeless, rotten branches that have fallen off the tree. If Baptism is the sacrament whereby someone becomes a member of the one and only true Church, how could baptism by heretics justify anyone? Thus St. Cyprian taught that those baptized by heretics were not really baptized and therefore must be rebaptized.
4. However, the view of St. Stephen I, Bishop of Rome, prevailed, and the Church to this day teaches that Baptism by heretics is valid if the baptist observers the proper form, i.e., “in the name of the Father, and of the Son, and of the Holy Spirit” (Matthew 28:19).