How do the Law, the prophets, and the life of Christ all fit together?
The Law reveals sin and cannot justify, while the prophets witness God's righteousness apart from the Law. Christ's life builds on the Law and prophets and brings everything to His death, burial, and resurrection. So the Law, the prophets, and Christ's life all fit together in that progression.
Les explains that the Ten Commandments are beautiful and perfect, yet by the Law no flesh is justified; the Law only gives the knowledge or understanding of sin, because sin is breaking the Ten Commandments. Then verse 21 introduces something totally different: the righteousness of God without the Law. That righteousness is witnessed by the Law and the prophets, showing Paul was not coming as an imposter with a watered-down product. Everything builds on what came before: the Law and the prophets, then the life of Christ, and it all brings us to His death, burial, and resurrection. The world hates this because it wants to work for salvation and take pride in its accomplishments, but God hates pride.