I said that it is in the Nicene fathers, not that it was explicitly in the creed itself. The doctrine of
'inseparable operations' was a defining feature of the pro-Nicene side to which the major Nicene figures like the Cappadocians, Hilary, Ambrose, and Augustine all believed and had to defend against their opponents. Here are a few quotes from them and more:
Since then the Holy Trinity fulfills every operation in a manner similar to that of which I have spoken, not by separate action according to the number of the Persons, but so that there is one motion and disposition of the good will which is communicated from the Father through the Son to the Spirit . . . But in the case of the Divine nature we do not similarly learn that the Father does anything by Himself in which the Son does not work conjointly, or again that the Son has any special operation apart from the Holy Spirit; but every operation which extends from God to the Creation, and is named according to our variable conceptions of it, has its origin from the Father, and proceeds through the Son, and is perfected in the Holy Spirit. For this reason the name derived from the operation is not divided with regard to the number of those who fulfill it, because the action of each concerning anything is not separate and peculiar, but whatever comes to pass, in reference either to the acts of His providence for us, or to the government and constitution of the universe, comes to pass by the action of the Three — Gregory of Nyssa, "To Ablabius."
just as Father and Son and Holy Spirit are inseparable, so do they work inseparably. This is also my faith inasmuch as it is the Catholic faith. — Augustine, "De Trinitate."
We have frequently said, however, that the operations of the Trinity are inseparable. — Augustine, "Commentary on the Gospel of John."
Lastly, that one may not think in that there is any difference of work either in time or in order between the Father and the Son, but may believe the oneness of the same operation, He says: “The works which I do, He doeth.” And again, that one may not think that there is any difference in the distinction of the works , but may judge that the will, the working, and the power of the Father and the Son are the same, Wisdom says concerning the Father: “For whatsoever things He doeth, the Son doeth the same likewise.” So that the action of neither Person is before or after that of the Other, but the same result of one operation. And for this reason the Son says that He can do nothing “of Himself,” because His operation cannot be separated from that of the Father. In like manner the operation of the Holy Spirit is not separated. Whence also the things which He speaks, He is said to “hear” from the Father. — Ambrose, "On the Holy Spirit."
And since He wished, therefore, to confess the power of his nature He stated: ‘This Son can do nothing of Himself, but only what He sees the Father doing’ . . . Because He was aware of His Father's power and strength that was with Him, the Son asserted that He could do nothing by Himself except what He saw the Father doing . . . all the things that the Father does the Son does in a like manner. This is the understanding of the true birth and the most complete mystery of our faith — Hilary of Poitiers, "De Trinitate."
For when some time ago, as now again, the heretics’ venom began to creep in, and the Arians’ blasphemy especially had begun to emerge, our predecessors, bishops together with legates from the city of the most holy bishop of Rome, were brought together in council at Nicaea … and drove out the deadly cups with this antidote, so that it was proper to believe that the Father, the Son and the Holy Spirit are of one Godhead, one power, one form, one substance. For we all say with one voice that the Trinity is of one power, one majesty, one Godhead, one substance so as to be an inseparable power . . . We assert that the Son is not dissimilar in operation, not dissimilar in power, or in anything at all dissimilar … Let us also confess that the Holy Spirit is uncreated but of one majesty, one substance, one power with God the Father and our Lord Jesus Christ. — Pope Damasus, "Epistle 2."
For we confess this Blessed Trinity to be One God for this reason, because in these three Persons there is no diversity either of substance, or of power, or of will, or of operation. — Pope Leo the Great, "Sermon 75."
The Holy Trinity has therefore the same Operation, and whatsoever things the Father doth and willeth to accomplish, these things doth the Son too in equal manner, likewise the Spirit also. But the giving of the Operations severally to Each of the Persons individually is nought else than to set forth three gods severally and wholly distinct from one another. For the count of Natural Unity in regard to the Holy Trinity, shews I suppose one motion unto every thing that is done. But if now we say that while One Person is moved, e.g., to work, the Two remain ineffective, how is not a gross severance privily introduced, allotting as a certain position to each Person, the being conceived of external to and isolated from the rest, not in respect of His Individual Being (for that were true), but in respect of utter diversity which does not endure language that gathers them into Natural Union? For One Nature of Godhead is conceived of in the Holy and Consubstantial Trinity. — Cyril of Alexandria, "Five Tomes Against Nestorius."
The Catholic Church has kept itself away from all these, as from so many pitfalls, and, instructed by the Holy Trinity, it teaches rightly and religiously and cries out: We believe in Father and Son and Holy Ghost; one Godhood in three hypostases; one will, one operation, alike in three persons; By the three Persons we understand that God is uncompounded and without confusion; by the consubstantiality of the Persons and their existence in one another and by the indivisibility of the identity of will, operation, virtue, power, and, so to speak, motion we understand that God is one . . .
For, here, that which is common and one is considered in actuality by reason of the co-eternity and identity of substance, operation, and will, and by reason of the agreement in judgment and the identity of power, virtue, and goodness-I did not say similarity, but identity - and by reason of the one surge of motion. For there is one essence, one goodness, one virtue, one intent, one operation, one power-one and the same, not three similar one to another, but one and the same motion of the three Person . . . For with the uncircumcised Godhead we cannot speak of any difference in place, as we do with ourselves, because the Persons exist in one another, not so as to be confused, but so as to adhere closely together as expressed in the words of the Lord when He said: 'I in the Father and the Father in me.' Neither can we speak of a difference in will, or judgment, or operation, or virtue, or any other whatsoever of those things which in us give rise to a definite real distinction. For that reason, we do not call the Father and the Son and the Holy Ghost three Gods, but one God — John of Damascus, "Fount of Knowledge."
And here are a few quotes from some modern historians/theologians:
One of the most important principles shared by pro-Nicenes is that whenever one of the divine persons acts, all are present, acting inseparably. — Lewis Ayres, "Nicaea and Its Legacy," p. 280
The inseparable operation of the three irreducible persons is a fundamental axiom of those theologies which provide the context for the Council of Constantinople in AD 381 and for the reinterpretation of Nicaea, which came to be the foundation of orthodox or catholic theology at the end of the fourth century. Lewis Ayres, "The Fundamental Grammar of Augustine's Trinitarian Theology."
The anti-Arian polemics of the fourth century eventually gave rise to a consensus Trinitarian grammar, often referred to as pro-Nicene theology, by which the unity of God is understood in terms of one divine essence common to all three persons. Understood as a consequence of this account of divine unity, the doctrine of the inseparable operations of the Trinity ad extra contends that all of the works of the Triune God with respect to the creation are works of all three persons of the Godhead. This doctrine, often expressed by the Latin axiom, opera trinitatis ad extra sunt indivisa has been a staple of orthodox Trinitarian theology for centuries. Statements and defense of the doctrine can be found among the Church fathers of the East (e.g. Athanasius and Gregory of Nyssa) and the West (e.g. Hilary of Poitiers and Augustine) as they engaged in anti-Arian polemical discourse. The doctrine is later expressed and defended by the medieval giant Thomas Aquinas and is fully embraced by the seventeenth-century Reformed Orthodox in their polemical engagement with the Socinians. The nineteenth-century heirs and defenders of Reformed Orthodoxy (e.g. Herman Bavinck and Charles Hodge) also held to this doctrine without wavering. — Kyle Claunch, "What God Hath Done Together."
One of the key axioms of pro-Nicene theology is the the "inseparable operation" of the divine persons, Anti-Nicenes argued that the distinct activity of the divine persons meant that Father, Son, and Holy Spirit are separate beings, with the Father being ontologically superior. In response pro-Nicenes like Ambrose and Hilary argued that Scripture demonstrates that all three persons are involved in acts of creation, providence and redemption. Thus, Father, Son and Holy Spirit share one nature. The inseparable action of the divine persons represents one of the fundamental elements of Augustine's trinitarian grammar. — Keith E. Johnson, "Rethinking the Trinity and Religious Pluralism: An Augustinian Assessment," p. 53.