"The authority of Pope Stephen I has been alleged for the validity of baptism given in the name of Christ only. St. Cyprian says (Epistle 72) that this pontiff declared all baptism valid provided it was given in the name of Jesus Christ. It must be noted that the same explanation applies to Stephen's words as to the Scriptural texts above given. Moreover, Firmilian, in his letter to St. Cyprian, implies that Pope Stephen required an explicit mention of the Trinity in baptism, for he quotes the pontiff as declaring that the sacramental grace is conferred because a person has been baptized "with the invocation of the names of the Trinity, Father and Son and Holy Ghost".Denzinger:
ST. STEPHAN I 254-257
The Baptism of Heretics *
[Fragment of a letter to Cyprian, from his letter (74) to Pompey]
46 (1) . . . "If therefore any come to you from any heresy whatsoever, let nothing be renewed except what has been transmitted, so that the hand is placed upon them for repentance, since the heretics among themselves properly do not baptize those coming to them, but only give them communion."
[Fragment from a letter of Stephan from a letter
(75) of Firmilianus to Cyprian]
47 (18) "But," he [STEPHAN] says, "the name of Christ conduces greatly to faith and to the sanctification of baptism, so that whoever has been baptized anywhere in the name of Christ, at once obtains the grace of Christ."