Irenaeus of Lyons also identifies the Angel/Messenger of the Lord with God the Son in Exodus 3:8:
And again, when the Son speaks to Moses, He says, I have come down to deliver this people.” Against Heresies III, 6.
Saint Hilary of Poitiers writes:
To discriminate clearly between the Persons, He is called the Angel of God; He Who is God from God is also the Angel of God, but, that He may have the honour which is His due, He is entitled also Lord and God. On the Trinity IV
Theodoret of Cyrus writes:
The whole passage (Exodus 3) shows that it was God who appeared to Moses. But Moses called Him an “angel” in order to let us know that it was not God the Father whom he saw — for whose angel could the Father be? — but the Only-begotten Son, the Angel of Great Counsel.”
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For more references to the Angel/Messenger of the Lord as the Pre-Incarnate Christ see also:
Justin Martyr, Dialogue with Trypho, 58, 59, 60, 61, 76, 86, 116, 126, 127, 128; Irenaeus, Against Heresies, 3.6.1-5, Fragments, 53; Tertullian, Against Praxeas, 16, De Carne, 14, Against Marcion 2.27, 3.9; Novatian, On the Trinity, 18, 19, 31; Apostolic Constitutions, 5.3.20; Clement of Alexandria, The Instructor, 1.7; Eusebius, The Proof of the Gospel, 1.5, 4.10, 5.10, Church History, 1.2.7-8, Preparation for the Gospel, VII. 5, 14-15; Origen, Contra Celsus, 5.53, 8.27; Methodious, Symposium, 3.4; Melito, New Fragments, 15; Ambrose, Exposition of the Christian Faith, 1.13.83; Athanasius, Against the Arians, 3.25.12-14; Gregory of Nyssa, Against Eunomius, 11.3.
Is the Angel of the Lord the Pre-Incarnate Christ? - Taylor Marshall