Commenting on the salvific efficacy of water baptism, Theophilus of Antioch wrote:
On the fifth day the living creatures which proceed from the waters were produced, through which also is revealed the manifold wisdom of God in these things; for who could count their multitude and very various kinds? Moreover, the things proceeding from the waters were blessed by God, that this also might be a sign of men's being destined to receive repentance and remission of sins, through the water and laver of regeneration,--as many as come to the truth, and are born again, and receive blessing from God. But the monsters of the deep and the birds of prey are a similitude of covetous men and transgressors. For as the fish and the fowls are of one nature,--some indeed abide in their natural state, and do no harm to those weaker than themselves, but keep the law of God, and eat of the seeds of the earth; others of them, again, transgress the law of God, and eat flesh, and injure those weaker than themselves: thus, too, the righteous, keeping the law of God, bite and injure none, but live holily and righteously. But robbers, and murderers, and godless persons are like monsters of the deep, and wild beasts, and birds of prey; for they virtually devour those weaker than themselves. The race, then, of fishes and of creeping things, though partaking of God's blessing, received no very distinguishing property. (Theophilus to Autolycus, Book II chapter xvi)
Such is consistent with the soteriology of his contemporaries; in the writings of Irenaeus of Lyons, for instance, we read:
3. Now, that we may not suffer ought of this kind, we must needs hold the rule of the faith without deviation,7 and do the commandments of God, believing in God and fearing Him as Lord and loving Him as Father. Now this doing is produced by faith: for Isaiah says: If ye believe not, neither shall ye understand. And faith is produced by the truth; for faith rests on things that truly are. For in things that are, as they are, we believe; and believing in things that are, as they ever are, we keep firm our confidence in them. Since then faith is the perpetuation of our salvation, we must needs bestow much pains on the maintenance thereof, in order that we may have a true comprehension of the things that are. Now faith occasions this for us; even as the Elders, the disciples of the Apostles, have handed down to us. First of all it bids us bear in mind that we have received baptism for the remission of sins, in the name of God the Father, and in the name of Jesus Christ, the Son of God, who was incarnate and died and rose again, and in the Holy Spirit of God. And that this baptism is the seal of eternal life, and is the new birth unto God, that we should no longer be the sons of mortal men, but of the eternal and perpetual God; and that what is everlasting and continuing is made God; and is over all things that are made, and all things are put under Him; and all the things that are put under Him are made His own; for God is not ruler and Lord over the things of another, but over His own; and all things are God's; and therefore God is Almighty, and all things are of God.
4. For it is necessary that things that are made should have the beginning of their making from some great cause; and the beginning of all things is God. For He Himself was not made by any, and by Him all things were made. And therefore it is right first of all to believe that there is One God, the Father, who made and fashioned all things, and made what was not that it should be, and who, containing all things, alone is uncontained. Now among all things is this world of ours, and in the world is man: so then this world also was formed by God.
5. Thus then there is shown forth One God, the Father, not made, invisible, creator of all things; above whom there is no other God, and after whom there is no other God. And, since God is rational, therefore by (the) Word He created the things that were made; and God is Spirit, and by (the) Spirit He adorned all things: as also the prophet says: By the word of the Lord were the heavens established, and by his spirit all their power. Since then the Word establishes, that is to say, gives body and grants the reality of being, and the Spirit gives order and form to the diversity of the powers; rightly and fittingly is the Word called the Son, and the Spirit the Wisdom of God. Well also does Paul His apostle say: One God, the Father, who is over all and through all and in us all. For over all is the Father; and through all is the Son, for through Him all things were made by the Father; and in us all is the Spirit, who cries Abba Father, and fashions man into the likeness of God.4 Now the Spirit shows forth the Word, and therefore the prophets announced the Son of God; and the Word utters the Spirit, and therefore is Himself the announcer of the prophets, and leads and draws man to the Father.
6. This then is the order of the rule of our faith, and the foundation of the building, and the stability of our conversation: God, the Father, not made, not material, invisible; one God, the creator of all things: this is the first point of our faith. The second point is: The Word of God, Son of God, Christ Jesus our Lord, who was manifested to the prophets according to the form of their prophesying and according to the method of the dispensation of the Father: through whom all things were made; who also at the end of the times, to complete and gather up all things, was made man among men, visible and tangible, in order to abolish death and show forth life and produce a community of union between God and man. And the third point is: The Holy Spirit, through whom the prophets prophesied, and the fathers learned the things of God, and the righteous were led forth into the way of righteousness; and who in the end of the times was poured out in a new way upon mankind in all the earth, renewing man unto God.
7. And for this reason the baptism of our regeneration proceeds through these three points: God the Father bestowing on us regeneration through His Son by the Holy Spirit. For as many as carry (in them) the Spirit of God are led to the Word, that is to the Son; and the Son brings them to the Father; and the Father causes them to possess incorruption. Without the Spirit it is not possible to behold the Word of God, nor without the Son can any draw near to the Father: for the knowledge of the Father is the Son, and the knowledge of the Son of God is through the Holy Spirit; and, according to the good pleasure of the Father, the Son ministers and dispenses the Spirit to whomsoever the Father wills and as He wills. (The Demonstration of the Apostolic Preaching, 3-7)
It happens that their tradition respecting redemption is invisible and incomprehensible, as being the mother of things which are incomprehensible and invisible; and on this account, since it is fluctuating, it is impossible simply and all at once to make known its nature, for every one of them hands it down just as his own inclination prompts. Thus there are as many schemes of "redemption" as there are teachers of these mystical opinions. And when we come to refute them, we shall show in its fitting-place, that this class of men have been instigated by Satan to a denial of that baptism which is regeneration to God, and thus to a renunciation of the whole [Christian] faith. (Against Heresies, 2.21.1)
It certainly was in the power of the apostles to declare that Christ descended upon Jesus, or that the so-called superior Saviour [came down] upon the dispensational one, or he who is from the invisible places upon him from the Demiurge; but they neither knew nor said anything of the kind: for, had they known it, they would have also certainly stated it. But what really was the case, that did they record, [namely,] that the Spirit of God as a dove descended upon Him; this Spirit, of whom it was declared by Isaiah, "And the Spirit of God shall rest upon Him," as I have already said. And again: "The Spirit of the Lord is upon Me, because He hath anointed Me." That is the Spirit of whom the Lord declares, "For it is not ye that speak, but the Spirit of your Father which speaketh in you." And again, giving to the disciples the power of regeneration into God, He said to them, "Go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost." For [God] promised, that in the last times He would pour Him [the Spirit] upon [His] servants and handmaids, that they might prophesy; wherefore He did also descend upon the Son of God, made the Son of man, becoming accustomed in fellowship with Him to dwell in the human race, to rest with human beings, and to dwell in the workmanship of God, working the will of the Father in them, and renewing them from their old habits into the newness of Christ. (Against Heresies, 3.17.1)