One of the greatest and rather extended debates of the early Church was on the doctrine of the Trinity. After hundreds of years and numerous church councils the Church Fathers finally formulated the doctrine of the Trinity, as we know it. The final clarifying statement on the Holy Spirit came when the Church confirmed the belief that the Holy Spirit proceeds from the Son as well as from the Father.
This clause is essential to our understanding of the application of redemption. The apostles used the term, “Spirit of Christ” in their New Testament writings. They had lived and worked with Jesus during His earthly ministry and when they saw the Spirit work after Pentecost they instinctively associated the Spirit of Pentecost with Christ. This is what Jesus had promised them; “… the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.” (John 14:26 cf. 16:13)
The Holy Spirit does not just instruct the intellect about Christ, He ministers the work of Christ in the heart and produces the grace of Christ into the life (Galatians 5:22f) in such a way that the experience of the Spirit is the experience of Christ—it is then, as Paul said, “Christ in you” (Col. 1:27).
“When a person becomes a Christian and has authentic faith, he has a real mystical union with Christ, so that Christ really comes to indwell the believer. When we exercise faith in Jesus Christ, His righteousness is counted towards us and we are justified. At that same moment, Christ, by virtue of the Holy Spirit, comes to dwell inside of us.”—R. C. Sproul