It’s not even our faith that we rely on, it’s Christ’s faith within us.
Look at the text below. Notice that it’s not “our” faith but Christ’s faith in us that we live.
Paul says, “I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith OF the Son of God, who loved me, and gave himself for me.” (Galatians 2:20 AV)
It is Jesus’ faith working in us who believe. So, we see that our righteousness is not IN Christ, but OF Him. And if so, we become part with Him, and He IN us.
But of him are ye in Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption: That, according as it is written, He that glorieth, let him glory in the Lord. (1 Corinthians 1:30-31 AV)
“Being filled with the fruits of righteousness, which are by Jesus Christ, unto the glory and praise of God.” (Philippians 1:11 AV)
And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: (Philippians 3:9 AV)
2 Corinthians 5:20-21 Therefore, we are ambassadors for Christ, God making his appeal through us. We implore you on behalf of Christ, be reconciled to God. For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.