To understand how the spirit proceeds from "the Son", first you must understand the nature of the Spirit. A fresh perspective may clear this up for you. Consider that originally Adam was made for everlasting life. So prior to the fruit of the knowledge of function and dysfunction. Adam was filled with the Holy Spirit for he also was with God.
Genesis 2:19 NKJV
Out of the ground the Lord God formed every beast of the field and every bird of the air, and brought them to Adam to see what he would call them. And whatever Adam called each living creature, that was its name.
I consider it Holy because it was approved of by God.
Genesis 1:31 NKJV
Then God saw everything that He had made, and indeed it was very good. So the evening and the morning were the sixth day.
What made Adam's spirit unholy was the fruit of the knowledge of Function and Dysfunction.
The fruit of the knowledge of Function is Pride.
The fruit of the knowledge of Dysfunction is Anxiety.
Thus we have arguments. Dysfunction pointed out by the daughters of Eve, and the Function pointed out by the sons of Adam. Now the Spirit of Peace and Comfort was active and unified before the argument. Once the argument starts however the spirit flees.
So the answer to our problem of Pride, Anxiety, and the Death that it brings. Is HUMILITY and FAITH. For humility is polar to pride, and faith is polar to anxiety.
Conclusion The Spirit of Love has always Existed with God and is God.
"God is Spirit, and those who worship Him must worship in spirit and truth." (John 4:24 NKJV)
Procession means "The act of moving forward." Without Humility and Faith, the Holy Spirit was not moving forward (from a certain perspective). Once Jesus did his thing then the Spirit was able to do his thing again.
There is only One God. "The Thinker(Father) that Said(Son) and Felt Love(Holy Spirit) from the beginning that came in flesh(Son) died, and rose again(Thinker thought of himself again)."
Note: So realize the question about the Spirit's co-equality. Is like asking me "Do you feel that your joy is as important as your thought? Or did the joy come from the thought? Or did the thought come from the joy? Or would you conclude that Joy is not as important as thinking? Or is what you say more important then your joy?
Answer: They are all important because they are His!