Doctrinal Proof
(1) God is one in His Being.
(2) All the three Persons possess all of the divine Being.
(3) Therefore all three Persons indwell each other fully.
The Father (as Father with His personal properties as not begotten nor proceeding) abides in the Son and in the Spirit.
The Son (as Son with His personal properties as begotten and not proceeding) abides in the Father and in the Spirit.
The Spirit (as Spirit with His personal properties as not begotten but proceeding) abides in the Father and in the Son.
Thus the perichoresis is a logical implication of the doctrine of the Holy Trinity and necessarily flows from it.
Biblical Texts
John 10:37-38: “If I do not the works of my Father, believe me not. But if I do, though ye believe not me, believe the works: that ye may know, and believe, that the Father is in me, and I in him.”
John 14:10-11: “Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works. Believe me that I am in the Father, and the Father in me: or else believe me for the very works’ sake.”
John 17:21, 23: “That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me … I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.”
Three Persons
Father and Son (John 10:37-38; 14:10-11; 17:21, 23)
Holy Spirit (I Cor. 2:10-11: “But God hath revealed them unto us by his Spirit: for the Spirit searcheth all things, yea, the deep things of God. For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.”)
Preposition
“in” (not simply “with”)
Words
circumincession (Latin)
perichoresis (Greek)
Theologian
John of Damascus (c.675-c.750)
Article
John of Damascus and the Perichoresis
Audios
The Trinity and Dwelling (Belgic Confession 8)
The Mutual Indwelling of the Father and the Son (Heidelberg Catechism, Lord’s Day 8; John 13:31-14:21)
Book
David J. Engelsma, Trinity and Covenant: God as Holy Family, esp. pp. 67-70, 82-85