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Question: Is Jesus Christ the savior of other worlds?
Question: Is Jesus Christ the savior of other worlds?
Very little has been revealed on this subject
The closest we have to an authoritative statement is an inference from Doctrine and Covenants 76:
For we saw him [Jesus Christ], even on the right hand of God; and we heard [a] voice bearing record that he is the Only Begotten of the Father — that by him, and through him, and of him, the worlds are and were created, and the inhabitants thereof are begotten sons and daughters unto God. (verses 23–24.)
The generally accepted interpretation of this verse is that if Jesus is the creator of many worlds, and the inhabitants of these worlds are children of the Father (both by birth and by covenant), then Jesus must be their Savior. This is probably the understanding of the majority of Latter-day Saints.
This interpretation is strengthened by a poetic version of section 76 (probably written by WW Phelps, but with input from Joseph) in which the vision is restated:
And I give a great voice bearing record from heav'n,
He's the Savior and only begotten of God;
By him, of him, and through him, the worlds were all made,
Even all that career in the heavens so broad.
Whose inhabitants, too, from the first to the last.
Are sav'd by the very same Saviour of ours;
And, of course, are begotten God's daughters and sons
By the very same truths and the very same powers. 
Joseph Fielding Smith speculated that Jesus Christ might be the savior of other worlds
Joseph Fielding Smith said "Perhaps this is the reason Jesus Christ was sent here instead of some other world, for in some other world they would not have crucified Him, and His presence was needed here because of the extreme wickedness of the inhabitants of this earth" (The Signs of the Times, pg. 5)
Other leaders who have taught similar ideas
Other Church leaders have echoed the same ideas, indicating that it is by far the majority position among LDS leaders:
Thousands of years before He [the Savior] came upon earth, the Father had watched His course and knew that He could depend upon Him when the salvation of worlds should be at stake; and He was not disappointed.
Bruce R. McConkie
"Our Lord's jurisdiction and power extend far beyond the limits of this one small earth on which we dwell. He is, under the Father, the Creator of worlds without number. (Moses 1:33.) And through the power of his atonement the inhabitants of these worlds, the revelation says, 'are begotten sons and daughters unto God' (D&C 76:24), which means that the atonement of Christ, being literally and truly infinite, applies to an infinite number of earths."
Marion G. Romney
Jesus Christ, in the sense of being its Creator and Redeemer, is the Lord of the whole universe. Except for his mortal ministry accomplished on this earth, his service and relationship to other worlds and their inhabitants are the same as his service and relationship to this earth and its inhabitants....In short, Jesus Christ, through whom God created the universe, was chosen [as the Redeemer in the pre-earthly councils] to put into operation throughout the universe [God the Father]'s great plan 'to bring to pass the immortality and eternal life of man.'...All who have a true concept of Jesus Christ and who have received a witness by the spirit of his divinity are ever stirred by the records of his life. They see in all that he said and did confirmation of his universal Lordship, both as Creator and Redeemer." 
Russell M. Nelson
The mercy of the Atonement extends not only to an infinite number of people, but also to an infinite number of worlds created by Him.
Brigham Young, on the other hand, taught that each world had its own Adam and Eve, and its own savior
Brigham Young gave a sermon in General Conference on 8 October 1854 in which he espoused a different view:
Let me open the eyes of your understanding. There has never been a time when the creations of worlds commenced. They are from eternity to eternity in their creations and redemption. After they are organized they experience the good and the evil, the light and the dark, the bitter and the sweet as you and I do. There never was a time when there were not worlds in existence as this world is, and they pass through similar changes in abiding their creation preparatory to exaltation. Worlds have always been in progress, and eternally will be.
Every world has had an Adam and an Eve, named so simply because the first man is always called Adam and the first woman, Eve. And the oldest son has always had the privilege of being ordained, appointed and called to be the heir of the family if he does not rebel against the Father, and he is the Savior of the family. Every world that has been created has been created upon the same principle. They may vary in their varieties, yet the eternity is one: it is one eternal round. 
Brigham's statement is probably where our critics are getting the idea we believe in a different savior for each world. However, Brigham's statement doesn't settle the question. In the early Utah period, there was a great deal of exploration from the pulpit of the limits of LDS belief, but these sermons were not considered final or authoritative. Such ideas play little, if any, part in present-day LDS teaching or discussion.
- Joseph Smith, Times and Seasons 4 no. 6 (1 February 1843), 83, stanzas 19-20; emphasis added. off-site GospeLink (requires subscrip.) direct off-site. Michael Hicks argued that Joseph was not the author of the poetic paraphrase in "Joseph Smith, W. W. Phelps, and the Poetic Paraphrase of 'The Vision'," Journal of Mormon History 20/2 (1994): 63–84.
- Lorenzo Snow, Teachings of Lorenzo Snow, compiled by Clyde J. Williams, (Salt Lake City: Bookcraft, 1984), 93. ISBN 0884945170. As cited in Tad R. Callister, The Infinite Atonement (Salt Lake City, UT: Deseret Book, 2000).
- Bruce R. McConkie, Mormon Doctrine, 2nd edition, (Salt Lake City: Bookcraft, 1966). GL direct link
- Marion G. Romney, "Jesus Christ, Lord of the Universe," Improvement Era (November 1968), 46,48. As cited in Tad R. Callister, The Infinite Atonement (Salt Lake City, UT: Deseret Book, 2000).
- Russell M. Nelson, "The Atonement," Ensign (November 1996), 35. As cited in Tad R. Callister, The Infinite Atonement (Salt Lake City, UT: Deseret Book, 2000).
- Brigham Young, "For This Is Life Eternal," in Eldon Watson (editor), Brigham Young Addresses (1982), 2:230. Brigham Young made similar statements on other occasions; for example: "There is no time when worlds have not been created and exalted; there have always been an Adam and an Eve—the first man and woman, and their oldest son is heir, and should be our Savior. We have one Father and we all are brethren." Journal of the Southern Indian Mission—Diary of Thomas D. Brown, p. 87–89; Friday, 6th Octr. 1854. "President Young said there never was any world created & peopled nor never would be but what would be redeemed by the shedding of the blood of the savior of that world." Journal of Wilford Woodruff; Ms/f/115, Church Historical Department; 12 May 1867. "All worlds have their God, their Savior, their sin, their priesthood, and can choose which they like, but beginning man rejected the priesthood by assuming to be a law unto himself—all other things abide this law." Minutes of Meetings Held in Provo City; Film/979.2/Z99/v. 2, BYU Microfilm Room; Sunday, 2 p.m. 3 October 1869.