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But thanks be to God through Jesus Christ our Lord
This is the answer to the question in 7:24.
So then, I myself serve the law of God with my mind. However, with the flesh I serve the law of sin
The law of God and the law of sin are spoken of as if they were masters whom Paul serves as a slave. With the mind or intellect Paul chooses to please and obey God, and with the flesh or physical nature he chooses to disobey God and to sin. Alternate translation: "My mind chooses to please God by obeying the law of Moses, but my flesh chooses to disobey God and sin" (See: rc://en/ta/man/jit/figs-metaphor and rc://en/ta/man/jit/figs-explicit)
the law of God
These words refer to the law of Moses, which was God's commands in written form.
the law of sin
These words refer to the natural human desire to rebel against God and disobey him. Paul calls this a law because he has observed that this is the way people live. It is not a collection of written commands.