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Joseph Fielding Smith Jr. (10th prophet):
Without the shedding of blood there is no remission of sins. In the whole Jewish economy, there was nothing strangled permitted to be used, either as food; or for sacrifice; it was an abomination. If Jesus had been strangled, hanged, or poisoned, so that his blood had remained in him his death would have brought forth no atonement for the sins of the world. He himself might have been saved because he was holy, and needed no atonement; but if his blood had not been shed, he would not have become a Savior to others;


Source: Smith, Joseph Fielding. Answers to Gospel Questions. Vol. 3., Salt Lake City: Deseret Book, 1961. 106.




John Taylor (third prophet):
But what is the reason for all this suffering and bloodshed, and sacrifice? We are told that without shedding of blood is no remission of sins. This is beyond our comprehension. Jesus had to take away sin by the sacrifice of himself, the just for the unjust, but, previous to this grand sacrifice, these animals had to have their blood shed as types, until the great antitype should offer up himself once for all.


Source: Taylor, John. The Gospel Kindom. Ed. G. Homer Durham. 3rd ed. Salt Lake City: Bookcraft, 1944. 116.




The reason Christ needed His blood shed had to deal with Adam's state in the Garden of Eden.




The Atonement of Christ saved mankind and allowed us to be resurrected, but there's certain sins that a person can commit that are beyond Christ's power to redeem. This type is sin requires each individual to atone for their own soul.



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