Acts 13: ( talking about Jesus )
Act 13:37 But he, whom God raised again, saw no corruption.
Act 13:38 Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins:
Act 13:39 And by him all that believe are justified from all things, from which ye could not be justified by the law of Moses.
Galatians 3:24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
The point here being, that the law is not done away with, but to lead us unto Christ, so by faith in Christ, you are no longer under the law, but under the commandment of Christ, which is (John 15:12 This is my commandment, That ye love one another, as I have loved you.); therefore many parts of the law of Moses is still applicable, because many parts of the law has to do with loving your neighbor as yourself. But the parts in the law of Moses such as many food ordinances, circumcision, clean, unclean, tithes to the temple, etc are not applicable today.
Act 15:24 Forasmuch as we have heard, that certain which went out from us have troubled you with words, subverting your souls, saying, Ye must be circumcised, and keep the law: to whom we gave no such commandment:
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Act 15:28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things;
Act 15:29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well.
Gal 4:21 Tell me, ye that desire to be under the law, do ye not hear the law?
Gal 4:22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman.
Gal 4:23 But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise.
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Gal 4:28 Now we, brethren, as Isaac was, are the children of promise.
Gal 4:29 But as then he that was born after the flesh persecuted him that was born after the Spirit, even so it is now.
Gal 4:30 Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman.
Gal 4:31 So then, brethren, we are not children of the bondwoman, but of the free.
Many parts of the Mosaic Law are applicable, but they are not applicable as the Mosaic Law. In other words, do them because they are right. Don't do them because they are something that Moses wrote down.
For example, much of the Code of Hammurabi is morally right. But doing the right things because they are part of Hammurabi's code is silly. Do them because they are right. In addition, you can find all kinds of good laws in most of the major governments of the world. Yet, you don't do those laws because they are part of this or that government. You do them because they are good and right.