How does the righteousness of God establish the law?

Romans 3:31 highlights that rather than making the law void, justification by faith establishes it. When Christ fulfilled the demands of the law through His perfect obedience, He upheld the integrity and righteousness of the law. This establishment confirms that believers, through their union with Christ, have met the law's standards by His righteousness. Therefore, rather than dismissing the law, the gospel affirms its importance while showing that salvation is through faith in the One who perfectly obeyed it on our behalf.