The NT does not invalidate the OT. Jesus Christ is literally the God of the OT. Jesus came to end the self imposed curse against Israel, known as the book of the law, which was given to the Levites to administer over Israel, and a witness against them.
The New Covenant is the law written on our hearts by the holy spirit. Hebrews 10:16, Jeremiah 31.31 etc. Yes the gentiles are in the new covenant as Paul so eloquently tells us in Romans 2:
14 For when the Gentiles, which have not the law, DO BY NATURE (do naturally) THE THINGS CONTAINED IN THE LAW, these, having not the law, are a law unto themselves:
15 WHICH SHEW THE WORK OF THE LAW WRITTEN IN THEIR HEARTS, their conscience also bearing witness,
What is the new covenant? Hebrews 10: 16 states EXACTLY what the new covenant is. 16 This is the covenant that I will make with them after those days, saith the Lord, I WILL PUT MY LAWS INTO THEIR HEARTS, AND IN THEIR MINDS WILL I WRITE THEM.
HOW does God write his laws upon our hearts? HOLY SPIRIT at your baptism, makes you dead to sin and alive to righteousness... Romans 6 This is the gospel.. You can recognize those that are actually born again, because they naturally DO the law of God he has written upon their hearts. 1 John 2:3-4
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