On the nature of the Church, comprehending each local church as “The Church” as well – compositely – as each in unity as a singular Church inclusive of but not under the Bishop of Rome, I offer some early liturgies and other witnesses taken from The Ante-Nicene Fathers (Roberts and Donaldson, T.T & Clark, Vol. 7, reprinted by Eerdmans, 1994)
The Divine Liturgy of James, the Holy Apostle and Brother of the Lord contains the following:
Priest/pastor: “For the peace of the whole world, and the unity of all the holy churches of God”
To which the people reply: “Let us beseech the Lord.”
In The Divine Liturgy of the Holy Apostle and Evangelist Mark, the Disciple of the Holy Peter, the Priest/pastor opens with a prayer which contains the following:
All the influence of Satan, all the snares of wicked men, do Thou, O Lord, drive away from us, and from Your Holy Catholic and Apostolic Church
The priest/pastor prays for the leaders of the [orthodox church]:
We pray and beseech Thee to defend in Thy good mercy our most holy and blessed high priest our Father in God ______, and our most reverend Bishop __________. Preserve them for us through many years in peace . . . with all the orthodox bishops, elders, deacons, sub-deacons, readers, singers, and laity, with the entire body of the Holy and only Catholic Church. . . But all the enemies of Thy Holy Church put Thou speedily under their feet through the grace, mercy, and love of Thine only-begotten Son.
Later in liturgy, the priest/pastor says:
O Sovereign and Almighty God, the Father of our Lord Jesus . . . Preserve for us through many years our most holy and blessed Papas _______, and our most pious Bishop ___________ . . . with all the orthodox bishops, elders, deacons, sub-deacons, readers, singers, with the entire body of the holy Catholic and Apostolic Church. . . .
And further, in his Anaphoral prayer, the pastor says:
O King of kings and Lord of lords, defend the kingdom of Thy servant, our orthodox and Christ-loving sovereign [Constantine, apparently] whom Thou hast deemed worthy to reign over this land in peace, courage, and justice. . .
Be kind to him, O Lord, for the sake of Thy Holy Catholic and Apostolic Church, and all Thy Christ-loving people, that we too in his peaceful reign may live a calm and tranquil life, in all reverence and godliness.
Oh Lord our God, give peace to the souls of our fathers and brothers who have fallen asleep in Jesus, remembering our forefathers of old, our fathers, patriarchs, prophets, apostles, martyrs, confessors, bishops, and the souls of all the holy and just men whohave died in the Lord.
Especially remember those whose memory we this day celebrate, and our holy father Mark, the apostle and evangelist, who has shown us the way of salvation.
Later the priest/pastor offers incense and says:
Defend, O Lord, our most holy and blessed Papas _______ [i.e. Patriarch: the Bishop of Constantinople, the New Rome], whom Thou hast fore-ordained to rule over our most pious Bishop ________, that they through many years of peace may, according to Thy holy and blessed will, fulfill the sacred priesthood committed to their care, and dispense aright the word of truth.
Remember the orthodox bishops everywhere, the elders, deacons, sub-deacons, readers, singers, monks, virgins, widows, and laity.
Remember, O Lord, the holy city [Jerusalem] of our God, Jesus Christ; and all cities and all lands, and the peace and safety of those who dwell therein in the orthodox faith of Christ; and the imperial city [Rome]; and this city of ours, and all cities and all lands, and the peace and safety of those who dwell therein in the orthodox faith of Christ.
Be mindful, O Lord, of the return of the backsliding, and of every Christian soul that is afflicted and oppressed, and in need of Thy divine mercy and help.
Be mindful also of us, O Lord, Thy sinful and unworthy servants, and blot out our sins in Thy goodness and mercy.
Be mindful of me, Thy lowly, sinful, and unworthy servant, and in Thy mercy blot out my sins.
Be with us, O Lord, who minister unto Thy holy name.
Bless our meetings, O Lord.
Utterly uproot idolatry from the world.
Crush under our feet Satan, and all his wicked influence.
Humble now, as at all times, the enemies of Thy Church. . .
Do Thou bless a thousand times ten thousand Thy faithful and orthodox people while they do Thy holy will.
The service continues with the Deacon directing the people who are seated to stand, another prayer, and then the Deacon directed the congregation to turn to the east. More prayer from the Priest and response from the people is followed by the consecration of the sacrament which concludes with:
“Fill, O God, this sacrifice with Thy blessing, through the inspiration of Thy all-holy Spirit. or the Lord Himself, our God and universal King, Christ Jesus, reclining at meat the same night on which He delivered himself up for our sins and died in the flesh for all, took bread in His holy, pure, and immaculate hands, and lifting His eyes to His Father, our God, and the God of all, gave thanks; and when He had blessed, hallowed, and broken the bread, gave it to His holy and blessed disciples and apostles, saying: (Aloud) Take, eat.
And as the deacon prays earnestly, the priest says aloud:
For this is my body, which is broken for you, and divided for the remission of sins.
To conclude: each church, then (and all as a singular body), is defined not by association with the Roman Bishop, but by its affirmation of the Creeds: Apostolic, Nicene, Athanasian. No mention in those of the supremacy or domination of the Roman bishop.