Through Silvanus, our faithful brother, as I consider him, I have written to you briefly, exhorting, and testifying that this is the true grace of God in which you stand.
exhorting, and testifying that this is the true grace of God wherein ye stand: Peter himself states this was the purpose of the writing. Through exhortation and bearing witness to the truth, or the "true" grace of God, the apostle confirmed wherein they stood. He had been there; as an eyewitness he urges them to continue in the Faith.