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I was thinking more about the things such as animal sacrifices and temple rituals, which were law prior to Jesus. But he did say he came to fulfill the Law, thereby making those practices obsolete since He became the ultimate sacrifice.
There was actually a dispute among the early Christians about whether or not they were still subject to the Law. James, the brother of Jesus, who led the church in Jerusalem took the view that Christians should still follow it. St Paul, for whatever his motives might be (Josephus speculated that Paul was an agent of the Jewish elders whose job was to detach the Christians from the Jews, in hopes the whole thing would fizzle out), held the view that the Law was fulfilled and also that Christianity was open to Gentiles.