See, I have searched and searched under infallibility and I cannot find anything which says "the ECFs in consensus are infallible’.
I have found ecclesiastical authority (Popes, councils), the ordinary Magesterium (of which the ECFs are PART), but I cannot find a specific statement such as you gave. May I ask where you found it?
The New Catholic Encyclopedia has a very good section on the Fathers of the Church
here
Amongst other things it states '**We receive only, says St. Basil, what we have been taught by the holy Fathers; and he adds that in his Church of Caesarea the faith of the holy Fathers of Nicaea has long been implanted (Ep. cxl, 2). St. Gregory Nazianzen declares that he holds fast the teaching which he heard from the holy Oracles, and was taught by the holy Fathers. These Cappadocian saints seem to be the first to appeal to a real catena of Fathers. The appeal to one or two was already common enough; but not even the learned Eusebius had thought of a long string of authorities. St. Basil, for example (De Spir. S., ii, 29), cites for the formula “with the Holy Ghost” in the doxology, the example of Irenaeus, Clement and Dionysius of Alexandria, Dionysius of Rome, Eusebius of Caesarea, Origen, Africanus, the preces lucerariae said at the lighting of lamps, Athenagoras, Gregory Thaumaturgus, Firmilian, Meletius.
In the fifth century this method became a stereotyped custom. St. Jerome is perhaps the first writer to try to establish his interpretation of a text by a string of exegetes (Ep. cxii, ad Aug.). Paulinus, the deacon and biographer of St. Ambrose, in the libellus he presented against the Pelagians to Pope Zosimus in 417, quotes Cyprian, Ambrose, Gregory Nazianzen, and the decrees of the late Pope Innocent. In 420 St. Augustine quotes Cyprian and Ambrose against the same heretics (C. duas Epp. Pel., iv). Julian of Eclanum quoted Chrysostom and Basil; St. Augustine replies to him in 421 (Contra Julianum, i) with Irenaeus, Cyprian, Reticius, Olympius, Hilary, Ambrose, the decrees of African councils, and above all Popes Innocent and Zosimus. In a celebrated passage he argues that these Western writers are more than sufficient, but as Julian had appealed to the East, to the East, he shall go, and the saint adds Gregory Nazianzen, Basil, Synod of Diospolis, Chrysostom.
In the second book “Contra Julianum”, St. Augustine again cites Ambrose frequently, and Cyprian, Gregory Nazianzen, Hilary, Chrysostom; in ii, 37, he recapitulates the nine names (omitting councils and popes), adding (iii, 32) Innocent and Jerome. A few years later the Semipelagians of Southern Gaul, who were led by St. Hilary of Arles, St. Vincent of Lérins, and Bl. Cassian, refuse to accept St. Augustine’s severe view of predestination because “contrarium putant patrum opinioni et ecclesiastico sensui”. Their opponent St. Prosper, who was trying to convert them to Augustinianism, complains: “Obstinationem suam vetustate defendunt” (Ep. inter Atig. ccxxv, 2), and they said that no ecclesiastical writer had ever before interpreted Romans quite as St. Augustine did — which was probably true enough. The interest of this attitude lies in the fact that it was, if not new at least more definite than any earlier appeal to antiquity. Through most of the fourth century, the controversy with the Arians had turned upon Scripture, and appeals to past authority were few. But the appeal to the Fathers was never the most imposing locus theologicus, for they could not easily be assembled so as to form an absolutely conclusive test. On the other hand up to the end of the fourth century, there were practically no infallible definitions available, except condemnations of heresies, chiefly by popes.**.’
and again
'**It will be observed that many of the writers rejected in the Gelasian list lived and died in Catholic communion, but incorrectness in some part of their writings, e.g. the Semipelagian error attributed to Cassian and Faustus, the chiliasm of the conclusion of Victorinus’s commentary on the Apocalypse (St. Jerome issued an expurgated edition, the only one in print as yet), the unsoundness of the lost “Hypotyposes” of Clement, and so forth, prevented such writers from being spoken of, as Hilary was by Jerome, “inoffenso pede percurritur”. As all the more important doctrines of the Church (except that of the Canon and the inspiration of Scripture) may be proved, or at least illustrated, from Scripture, the widest office of tradition is the interpretation of Scripture, and the authority of the Fathers is here of very great importance. Nevertheless it is only then necessarily to be followed when all are of one mind: “Nemo . . . contra unanimum consensum Patrum ipsam Scripturam sacram interpretari audeat”, says the Council of Trent; and the Creed of Pius IV has similarly: “. . . nec eam unquam nisi juxta unanimum consensum Patrum accipiam et interpretabor”. The Vatican Council echoes Trent: “nemini licere . . . contra unanimum sensum Patrum ipsam Scripturam sacram interpretari.”
A consensus of the Fathers is not, of course, to be expected in very small matters: “Quae tamen antiqua sanctorum patrum consensio non in omnibus divinae legis quaestiunculis, sed solum certe praecipue in fidei regula magno nobis studio et investiganda est et sequenda” (Vincent, xxviii, 72). This is not the method, adds St. Vincent, against widespread and inveterate heresies, but rather against novelties, to be applied directly they appear. **’
I trust that answers your question
