"What purpose could there possibly be, in the Savior going to the spirit world to preach the gospel, if there were no provision in the gospel for deliverance of the dead? ... Surely not! There could be but one purpose for preaching the gospel to the dead, and that would be to "proclaim liberty to the captives, and the opening of the prison to them that are bound." The scriptures declare that God is no respecter of persons. As this doctrine is true, then there can come no condemnation to the dead, simply because they died without the opportunity of hearing and confessing Jesus Christ. Justice demands that all such shall have the same opportunity to hear, to repent and accept the gospel which is offered to those who are living in the flesh. Provision has been made by which the gospel message is proclaimed among these active spirits, and provision has been made in the gospel plan, appointed before the foundation of the earth was laid, for the vicarious work to be performed for them, if in that spirit world they repent and receive the gospel. Otherwise God would be a respecter of persons favoring the living and condemning the dead, who would be penalized when dying without the opportunity to receive the gospel.
Joseph Fielding Smith
The case for Christian belief in Salvation for the Dead is found here