Jesus when He claimed to be the Son of God told the people “I and the Father are one.” (John 10:30)

The wording in Greek is literally we are one. Jesus is not teaching a Bible theology course but making a defense to those challenging him on who He is. So the Holy Spirit, the comforter is excluded in this statement.

Some make too much of this one statement; we need to bring in other scriptures that would clarify this.

John 6:38 Jesus states, “For I have come down from heaven, not to do My own will, but the will of HIM WHO SENT ME.”(same as Heb.10:5). Jesus also said, John 14:28 Ye have heard how I said unto you, I go away, and come again unto you. If ye loved me, ye would rejoice, because I said, I go unto the Father: for my Father is greater than I.”

This greater means in position, not nature, as He came as a servant among men.

The same that is said of the Father and the Son can be said of the Holy Spirit, the comforter.

Jesus also said he would send another like himself from heaven. Thus, if He is one with the Father so is this other one He will send. As he is a person  so is the Holy Spirit. The Holy Spirit is sent just as the Son was sent by another (the Father) from heaven.

Jesus  asked the Father to send another comforter (Greek- Allos paracletos) which means another of the same kind, (stock, generation.) Someone does not ask himself to do something.

The word allos ‘another” is used 34 times in John’s Gospel; every time it is used personal subjects are in view showing distinction and differences. It shows a difference between one speaking and the other he is speaking to, or asking. To give a illustration, in Jn.20:17 Jesus tells Mary” I have not yet ascended to my Father, but go to my brethren and say to them…” All these are personal subjects and have the same meaning. He tells Mary to tell the brethren, they are different from Jesus, just as he is going to the Father, who is different. She is going to a different party from herself, just as Jesus is going to a different party than himself.

This other one, called the Holy Spirit stays invisible (except for some manifestations) and will bear witness to the Son and his words, just as the son bears witness to the Father. He is sent to be with us as Jesus was to them when he was physically here on earth.

John 5:43 “I have come in My Father's name,” Greek- ego erchomai- I come 1) to come; used of persons: to come from one place to another, and used both of persons arriving 2) to appear, make one's appearance, to come before the public. This in fact proves them to be two different persons.

So how do we arrive at the third person as being one as (the son) Jesus and the Father are one?

First, they are all eternal, they are all taking part in creation.

John 14:26"But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things

He is sent from heaven as the Son, who is eternal alongside the Father (Jn.3:16, 6:39, 12:49).

Robertson's Word Pictures: “And I will pray the Father (kagw erwthsw ton patera). Erwtaw for prayer, not question (the old use), also in 1 John 16:23 (prayer to Jesus in same sense as aitew), 1 John 14:26 (by Jesus as here); 1 John 17:9 (by Jesus), "make request of." Another Comforter (allon paraklhton). Another of like kind (allon, not eteron ), besides Jesus who becomes our Paraclete, Helper, Advocate, with the Father (1 John 2:1, Cf. Romans 8:26). This old word (Demosthenes), from parakalew, was used for legal assistant, pleader, advocate, one who pleads another's cause (Josephus, Philo, in illiterate papyrus), in N.T. only in John's writings, though the idea of it is in Romans 8:26-34. Cf. Deissmann, Light, etc., p. 336. So the Christian has Christ as his Paraclete with the Father, the Holy Spirit as the Father's Paraclete with us (John 14:16,26; John 15:26; John 16:7; 1 John 2:1).

Jamieson, Fausett and Brown: ‘he shall give you another Comforter--a word used only by John; in his Gospel with reference to the Holy Spirit, in his First Epistle (1 John 2:1), with reference to Christ Himself. Its proper sense is an "advocate," "patron," "helper." In this sense it is plainly meant of Christ (1 John 2:1), and in this sense it comprehends all the comfort as well as aid of the Spirit's work. The Spirit is here promised as One who would supply Christ's own place in His absence.

Vincent's Word Studies: "The Holy Spirit is to be another Paraclete, and this falls in with the statement in the First Epistle, "we have an advocate with God, even Jesus Christ." Compare Rom. viii. 26. See on Luke vi. 24. Note also that the word another is allon, and not eteron, which means different. The advocate who is to be sent is not different from Christ, but another similar to Himself."

Another (allos) means more than one with all being of the same like character or a different one in the character of the first. Allos expresses a numerical difference and denotes "another of the same sort;" heteros expresses a qualitative difference and denotes "another of a different sort." Christ promised to send "another Comforter" (allos, "another like Himself," not heteros, which makes them completely different).

All through the bible the Triunity is inherent in the revelation of God. The one eternal God has revealed that within His nature of one (echad) are three distinctions, three distinct in consciousness that are personal. These identities are 3 persons. These personal distinctions are eternal and simultaneously existing.

It is not based on any single passage of Scripture but all the revelation found throughout the Scripture. The early Church pastors who defended the faith against heresies put these together as doctrine on the nature of God from studying the Scripture. Some were directly linked to the apostles. We need to understand God used words in scripture to accommodate our human understanding, not just for this doctrine but others.

We believe in ONE God and within His essence of being (his nature) there eternally and simultaneously exists three personal subjects; The Father The son (also called the Word and the Holy Spirit (also called the comforter)

Distinct in that: the Father is not the Son nor is the Son the Father, and the Holy Spirit (the comforter) is neither the Father nor the Son.

The Holy Spirit was involved in the creation; (Ps. 104:30, Job 26:13 “By His Spirit He made the heavens” (Job 33:4). He too shares in the one essence that is God, being full deity, as the Son and the Father are.

He was there in the beginning of creation and is still with us today. He is the gift of eternal life to the believer. He is called the eternal Spirit (Heb.9:14), as well as the giver of life (Romans 8:2). In Ps.139 there are three omni’s mentioned for the Spirit, omnipotence, omnipresence, omniscience, all are attributes belonging only to God. He is omnipresent, since He would dwell in every believer simultaneously, and throughout history. Furthermore and most important is that He, the Holy Spirit is called God in 1 Cor.6:19, and rightly so, as Jesus also said in John 4:24 “God is Spirit.”

The Father has an eternal nature, the Son has the same eternal nature and the Holy Spirit does.

Eph. 1:17 that the God of our Lord Jesus Christ, the Father of glory, may give to you the spirit of wisdom and revelation in the knowledge of Him”