God said to Moses, “I AM WHO I AM. This is what you are to say to the Israelites: ‘I AM has sent me to you.’”
God does not derive His life from any external source. He has life within Himself. This means that God exists independently of any cause. He has always existed, and will exist forever. Since no one has caused His existence, no one can make God's existence cease. This leads to the attribute of immortality.
There is no one passage that specifically declares God's self-existence. But, the attribute is implicit in many of the following verses:
10 “You are my witnesses,” declares the LORD, “and my servant whom I have chosen, so that you may know and believe me and understand that I am he. Before me no god was formed, nor will there be one after me. 11 I, even I, am the LORD, and apart from me there is no savior. NIV
12 Who has measured the waters in the hollow of his hand, or with the breadth of his hand marked off the heavens? Who has held the dust of the earth in a basket, or weighed the mountains on the scales and the hills in a balance? 13 Who has understood the mind of the LORD, or instructed him as his counselor? 14 Whom did the LORD consult to enlighten him, and who taught him the right way? Who was it that taught him knowledge or showed him the path of understanding? 15 Surely the nations are like a drop in a bucket; they are regarded as dust on the scales; he weighs the islands as though they were fine dust. 16 Lebanon is not sufficient for altar fires, nor its animals enough for burnt offerings. 17 Before him all the nations are as nothing; they are regarded by him as worthless and less than nothing. NIV
1 In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was with God in the beginning. 3 Through him all things were made; without him nothing was made that has been made. 4 In him was life, and that life was the light of men. 5 The light shines in the darkness, but the darkness has not understood it. NIV
For as the Father has life in himself, so he has granted the Son to have life in himself. NIV
1 In the beginning God created the heavens and the earth. 2 Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. 3 And God said, “Let there be light,” and there was light. NIV