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Romans 6:22 has a lot of "buts" in it. The NIV of the passage says, "But now that you have been set free from sin and have become slaves of God, the benefit you reap leads to holiness, and the result is eternal life." However, the more literal translation, while somewhat choppy, zeros in on the focus of the verse: "But now being freed from sin, but being enslaved to God, you are having/possessing your fruit into holiness, but the goal/end result into life eternal." There are two interesting features about holiness in Romans 6:22.
First, all the verbs are in the passive, which means that none of the action is being done by the human players. They definitely benefit from the action, but they themselves don't do the action; someone else freed them from sin and someone else has made them slaves to God. So the reality of holiness in the Christian life has nothing to do with us, but rather everything to do with what God is doing in our lives.
Second, the holiness that characterizes the Christian life seems to be something in tension - it is caught in a back-and-forth experience of dying to sin and coming to new life in Christ. We find ourselves in the process of being freed from sin, but we also find ourselves in the process of becoming God's slaves; we now have some of the fruit of holiness in our lives (cf. Galatians 5:22-23), but we will eventually have all the fruit of holiness in our lives - with holiness finally bringing forth the final outcome of eternal life.
Romans 6:22 emphasizes a familiar theme we've seen throughout the Bible: holiness primarily has to do with God and not behavior, since God is the Holy One who makes the rest of us holy. But Romans 6:22 also highlights the fact that holiness leads to eternal life. It doesn't give us eternal life, as if you could get eternal life by doing good deeds or acts of holiness; instead, the natural result or byproduct of holiness is eternal life - because holiness isn't designed to fit you for heaven, as much as holiness is the first step in a whole new way of existing (eternally vs. mortally).
As we worship God today, let us thank him for all he's done in our lives to give us holiness and lead us into eternal life with himself.