@Trofimus - Jesus uses the sacred name of God, or YHVH, which is "I am." Except it is not "I am" in Greek, but "I, I am" “ἐγώ ἐιμί!"
John in his gospel refutes these early heretics,and the Jews, with his 7 “I am” statements!
“I am the bread of life” John 6:35
“I am the light of the world.” John 8:12
“I am the door” John 10:9
“I am the Good Shepherd” John 10:11
“I am the resurrection and the life.” John 11:25
“I am the way, the truth and the life” John 14:6
“I am the true vine, my Father is the vinedresser” John 15:1
Now, while these are all expressive and interesting word pictures, but how do they prove the deity of Christ?
For example, looking at the first one more closely. John 6:35, for example says "Ἐγώ εἰμι ὁ ἄρτος τῆς ζωῆς·" "I am the bread of life." But please notice, he does not say Eimi, which would be the normal way to say "I am" in the rest of the Bible. Jesus specifically uses the sacred name of God, to refer TO HIMSELF.
Unfortunately, the Greek wording does not come out in any English translation that I am aware of. But the Greek is very important. The way to say, “I am” in Greek is εἰμί or eimi. Indeed, in each of the 7 “I am” verses I listed just a minute ago, the word “I” or ἐγώ” or ego is also included. Thus, in all 7 of these “I am” statements, John actually says, “ἐγώ ἐιμί” οr “I, I am.” So again, that is “ἐγώ ἐιμί.” Or just think “I, I am!” But even that is not enough to explain why these statements, among others, made the Pharisees and the scribes so angry, that they tried to stone Jesus for making himself equal with God.
We have to look back to the Old Testament to find the full reason. In Exodus 3:14 Moses asks God whom he is to say sent him to Pharaoh. YHWH gives his sacred name.
“God said to Moses, “I am who I am.” And he said, “Say this to the people of Israel, ‘I am has sent me to you.’” Ex. 3:14.
In Hebrew, “I am” is the tetrgram YHWH, or as some transliterate into English, Yahweh. A few hundred years before the time of Christ, Alexander the Great, when he ruled the known world, started a rigorous program of Hellenization (or making everyone into Hellenes or Greeks,) The Jews started were losing their Hebrew. So in Egypt, an ambitious project to translate the OT into Greek was started, for the Hellenized Jews, and completed around 300 years before the time of Christ.
So how do you think this Old Testament, which was called the Septuagint or LXX (After the 70 or 72 translators who translated the Hebrew into Greek), which Jesus and the disciples also used, translated “YHWH or יְהֹוָה ? In Greek, Exodus 3:14 was ἐγω ἐιμί. Repeat that ἐγω ἐιμί! The sacred name of God was translated as “I am” in exactly the same way John wrote that Jesus called himself at least 7 times, in the above statements. The Jehovah's witnesses translate "ego eimi," into the word Jehovah! But the Jews, before Christ, they translated YHWH into Greek using the words ἐγώ ἐιμί. in Exodus 3:14. I think they knew what they were talking about, and certainly Jesus knew what he was talking about, when he called himself the same name as God! And that is why the Jews were so angry with him they tried to stone him. He was calling himself God. He said before Abraham was ἐγώ ἐιμί or "I, I am." And then in his teaching he repeated the fact in his parables and metaphors that he was God. Because he said "ἐγώ ἐιμί" or "I, I am" or YHWH!"
It doesn't get any clearer than that!