How do we know that Jesus Christ is the believer's righteousness?

In Philippians 3:9, the Apostle Paul articulates a profound truth: believers are found in Christ, not having their own righteousness derived from the law, but that which is through faith in Christ. This truth is foundational to sovereign grace theology, which teaches that human efforts cannot attain righteousness. Instead, Christ’s perfect righteousness is credited to believers, allowing them to stand justified before God. This divine exchange is the heart of the gospel, illustrating that in Christ, the elect are clothed in His righteousness, identified as ‘the Lord our Righteousness’ (Jeremiah 23:6). Such understanding emphasizes the futility of self-righteousness and the glorious gift of grace bestowed upon those who believe.