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Is this passage contrasting how in the Old Administration of the Covenant people did not continue in it, and in the New Covenant they will not?
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No. It is contrasting the Mosaic explanation of "Dothis and live" to the unregenerate in covenant with God who broke the Law Covenant.
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What is Christ mediating to the unelect members of the Covenant?
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Covenant Curses.
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They no longer need to be led by God because God now indwells them.
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So in the OT people were not indwelt???
You may want to rethink all that.
Did Jesus believed that men like Abraham, or any Old Testament saint among the Israelites, were saved and indwelt by the Spirit having the law written on their hearts? Yes. Jesus says in John 3:3 and 5 that "Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God...Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God."
1 Peter 1:11 is quite plain, "Searching what, or what manner of time the Spirit of Christ which was in them did signify, when it testified beforehand the sufferings of Christ, and the glory that should follow." Here Peter is referring to the "prophets (verse 2)."
The Old Testament is full of verses speaking about the Law written on the heart, and the working of the heart in contemplation of that Law in this regard. The following are some samples:
Deuteronomy 4:39, "Therefore know this day, and consider it in your heart, that the LORD Himself is God in heaven above and on the earth beneath; there is no other.
Deuteronomy 6:6, "And these words which I command you today shall be in your heart."
Deuteronomy 8:2, "And you shall remember that the LORD your God led you all the way these forty years in the wilderness, to humble you and test you, to know what was in your heart, whether you would keep His commandments or not."
Deuteronomy 11:18, "Therefore you shall lay up these words of mine in your heart and in your soul, and bind them as a sign on your hand, and they shall be as frontlets between your eyes."
Deuteronomy 30:14, "But the word is very near you, in your mouth and in your heart, that you may do it."
Zechariah 8:17, "Let none of you think evil in your heart against your neighbor; And do not love a false oath. For all these are things that I hate,' Says the LORD."
Psalm 37:31, "The law of his God is in his heart; None of his steps shall slide."
Psalm 119:10, "With my whole heart I have sought You; Oh, let me not wander from Your commandments!"
Psalm 119:34, "Give me understanding, and I shall keep Your law; Indeed, I shall observe it with my whole heart."
Psalm 119:69, "The proud have forged a lie against me, But I will keep Your precepts with my whole heart."
There are also a number of Scriptures that deal with the law specifically said to be in the heart of God's Old Testament people. Again, here are some samples:
Isaiah 51:7, "Listen to Me, you who know righteousness, You people in whose heart is My law: Do not fear the reproach of men, Nor be afraid of their insults."
Psalm 40:8. "I delight to do Your will, O my God, And Your law is within my heart."
Proverbs 3:1, "My son, do not forget my law, But let your heart keep my commands."
Certainly, on the same note, the idea of regeneration is seen as the circumcised heart. Deut. 30:6 says, "And the LORD your God will circumcise your heart and the heart of your descendants, to love the LORD your God with all your heart and with all your soul, that you may live." Deut 10:16 also mentions this, "Therefore circumcise the foreskin of your heart, and be stiff-necked no longer." In Jeremiah 4:4 we find this statement, "Circumcise yourselves to the LORD, And take away the foreskins of your hearts, You men of Judah and inhabitants of Jerusalem, Lest My fury come forth like fire, And burn so that no one can quench it, Because of the evil of your doings." And it is clear that circumcision had a direct correlation to the heart even into the New Testament "but he is a Jew who is one inwardly; and circumcision is that of the heart, in the Spirit, not in the letter; whose praise is not from men but from God (Romans 2:29)." Even Romans 2:15 demonstrates that the Gentiles, in a base manner, had the law written on their hearts even though they were without the law, "who show the work of the law written in their hearts, their conscience also bearing witness..."