Book of Life is written about in both the Hebrew and New Testament Scriptures, a total of seven times. That is pretty convincing proof of the existence of the Book.

Exodus 32:32. Yet now, if You will forgive their sin, and if not, erase me, please, out of your Scroll which You have written.” (Rev. 21:27) 33. And the LORD* said to Moses, “Whoever has sinned against Me, I shall erase him from My Book.”