While commenting on the ordinance of the Lord's Supper, Russell M. Nelson made the following connection between the reception of eternal life and the sacrament, including an appeal to John 6:
The sacrament, like baptism, is such a sacred ordinance that it deserves greater comprehension. Scripture teaches us that “the life of the flesh is in the blood” (Leviticus 17:11; emphasis added). Shortly after man was cast out of the Garden of Eden, sacrifice was instituted wherein life was terminated by the shedding of blood. In our day, we observe that heart attack, stroke, and gangrene all follow in the wake as life leaves any part of the body deprived of its blood supply.
With that background, think of this passage from the gospel of John, “Except ye eat the flesh of the Son of Man, and drink is blood, ye have no life in you. Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day” (John 6:53-54; emphasis added).
In one ordinance, the emblems of His atoning sacrifice and His promise of resurrection to eternal life are symbolically recalled. Every week, we commemorate those events as we partake of the sacrament while renewing our covenants with the Lord. (“Twenty Questions,” Church Educational Systems, September 13, 1985, as quoted in Teachings of Russell M. Nelson [Salt Lake City: Deseret Book, 2018], 340)