"It's not if you take it out"
ok.. I know that was tongue in cheek, but...
If the concept is not systematically presented in the old covenant text, it does not exist in the new covenant text as doctrine.
Concoursely, if a concept is systematically presented in the old testament text, it is lawful as doctrine in the new, where context permits.
But the doctrine of saved by grace is systematically presented in the OT as well as the NT. (we're going to get spanked for derailing this) If you take the book of Ezekiel and look at the 26th chapter vs 13 to the end of the chapter you see a sovereign God who acts for his names sake for the benefit of his chosen people who have chosen to defile his name. This theme is reflected over and over again in Jacob and Esau, the life of David, and many many other stories involving the nation of Israel. God chose them - they rejected him - God pursued them - they rejected him - God acts to make up for their insufficient behavior. Eternal security is reflected in the nature of God's relationship to the nation of Israel - they are chosen and set aside not because of their good behavior but because of God's grace and mercy despite their behavior. Same for all of us NT believers.