Some of the most powerful affirmations of Jesus’ deity are a chain of expressions in John’s gospel known as the “I am” statements. Each of these phrases employs the name God revealed to Moses at the burning bush—“I AM” (Ex. 3:14). Jesus applied that name to himself in a series of prominent declarations: “I am the bread of life” (John 6:35). “I am the living bread that came down out of heaven” (6:51). “I am the light of the world” (8:12; 9:5). “I am the door of the sheep” (10:7). “I am the good shepherd” (10:11). “I am the resurrection and the life” (11:25). “I am the way, and the truth, and the life; no one comes to the Father, but through Me” (14:6). And this stunning, inescapable affirmation of deity: “Truly, truly, I say to you, before Abraham was born, I am” (8:58).

Jesus’ stature as the great I AM of the Old Testament was essential to his role as Savior. Those who refused to acknowledge him for who he is could not be saved: “Unless you believe that I am, you shall die in your sins” (8:24). This set up an extremely difficult barrier for Pharisees who were predisposed to hate him anyway. They understood that he was claiming authority over their greatest patriarchs and prophets (John 4:12; 8:53). Indeed, he was claiming equality with God, and the ramifications of that they could not accept. Therefore, Jesus warned them, they would die in their sins.

On the night before his death, alone with his disciples after Judas had departed to do his evil, turncoat, treacherous deed, the Lord revealed another aspect of his deity to the remaining disciples. And once again he used the highest name of God, I AM:

John 15:1-8
I am the true vine, and My Father is the vinedresser. Every branch in Me that does not bear fruit, He takes away; and every branch that bears fruit, He prunes it, that it may bear more fruit. You are already clean because of the word which I have spoken to you. Abide in Me, and I in you. As the branch cannot bear fruit of itself, unless it abides in the vine, so neither can you, unless you abide in Me. I am the vine, you are the branches; he who abides in Me, and I in him, he bears much fruit; for apart from Me you can do nothing. If anyone does not abide in Me, he is thrown away as a branch, and dries up; and they gather them, and cast them into the fire, and they are burned. If you abide in Me, and My words abide in you, ask whatever you wish, and it shall be done for you. By this is My Father glorified, that you bear much fruit, and so prove to be My disciples.

from The Gospel According to Jesus, John MacArthur