“And as for the resurrection of the dead, have you not read what was said to you by God: ‘I am the God of Abraham, and the God of Isaac, and the God of Jacob’? He is not God of the dead, but of the living.” (Matthew 22:31-32, also Mark 12:24-27).
Jesus is confronting those who did not believe that there was resurrection. More than that, they limited their recognition of God’s word to the first five books of our Christian Bible. Jesus uses God’s word, even the part they recognize, and proves the resurrection. But it’s not how we might do it now. It’s not an explicit teaching. Jesus does not rely on 1 Corinthians 15 or the like. Jesus uses the present tense of the verb to show that there is a resurrection from the dead.
In John 10:34-38 a similar situation comes up. It reads, “Jesus answered them, ‘Is it not written in your Law, “I said, you are gods”? If He called them gods to whom the word of God came—and Scripture cannot be broken— do you say of Him whom the Father consecrated and sent into the world, “You are blaspheming,” because I said, “I am the Son of God”? If I am not doing the works of my Father, then do not believe me; but if I do them, even though you do not believe me, believe the works, that you may know and understand that the Father is in me and I am in the Father.’”
Jesus is drawing from Psalm 82 where God confronts the judges of Israel who received God’s word in order to judge His people. God calls these judges “gods” because the word of God was given to them. These judges were not following the law though. Jesus draws a contrast between Himself and the judges. God calls the disobedient judges “gods”, so why would it be wrong for Jesus to be the “Son of God” when He is entirely obedient to God’s word? Jesus uses Psalm 82 as a point to jump off from to prove that He is not sinning but is, in fact, justified by His obedience to God’s word when He says “I am the Son of God”.
I bring these to your attention as examples of why we must pay attention to even the smallest details of the Bible. As Jesus shows, every part, even the implications, of the Bible are truly inspired by God. We need to press into our study of God’s word to unearth all that we can so that we might surely know “the only true God, and Jesus Christ whom [He has] sent” (John 17:3).
You may with to look into more quotes of the Old Testament by the New Testament here. The book Commentary on the New Testament Use of the Old Testament, edited by G. K. Beale and D. A. Carson (Baker Academic, 2007) has also been recommended to me for this subject. Maybe you can let me borrow it when you’re done reading it