Here are the three "Persons" of the Athanasian creed. Jesus appears to be subordinate because he prays to the Father, and the Comforter appears to be subordinate because he obeys the mandate of the Father. But let us note that it is the Comforter, or the Holy Spirit, who is to be sent. Immediately he tells us,
"I will not leave you comfortless: I will come to you."
In other words, he at once identifies himself with this Comforter. He confirms this a little later by saying,
"He that loveth me, shall be loved of my Father, and I will love him, and will manifest myself to him."
But he modifies this by saying,
"If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him."
First, it was the Holy Spirit who was to be sent; then it was Jesus who was to come and comfort his disciples; then both the Father and the Son are to come. Then he caps the climax by saying,
"But the Comforter, which is the Holy Spirit, whom the Father will send in my name."
