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"The law of Christ" is a New Testament phrase. The related Bible verses are in the Pauline epistles at Galatians 6:2 and parenthetically at 1 Corinthians 9:21.
Some Christians hold the belief that the crucifixion of Jesus Christ and the inauguration of the New Covenant of Jeremiah 31:31–37 and Ezekiel 37:22–28 "replaces" or "completes" or "fulfills" the Law of Moses found in the Hebrew Bible. Dual-covenant theologians, the Hebrew Roots Movement, and Messianic Judaism are all examples of a groups that reject this belief.
Closely related are the subjects of Christian views on the Old Covenant, early Christianity and Judaism, Paul the Apostle and Judaism, abrogation of old covenant laws, and Christian ethics.