D&C 88:2
“We receive the gospel, not that we may have our names written in the Lamb’s book of life, but that our names may not be blotted out of that book. ‘For,’ saith the Lord, ‘He that overcometh, the same shall be clothed in white raiment, and I will not blot out his name out of the book of life.’ Why? Because he had overcome through his faithfulness. My doctrine is—that there never was a son and daughter of Adam and Eve born on this earth whose names were not already written in the Lamb’s book of life, and there they will remain until their conduct is such that the angel who keeps the record is authorized to blot them out and record them elsewhere.” (Brigham Young, Journal of Discourses 12:101)