Jesus was baptized by John. That was, in his case, the fulfilment of all righteousness. (Acts 19:1) In all probability, they had been baptized with the baptism of John after the Christian baptism had been instituted and substituted for that of John, in which case their first baptism would have been invalid.
John the Baptist a great prophet. "The question arose from the saying of Jesus, ’Among those that are born of women there is not a greater prophet than John the Baptist; but he that is least in the kingdom of God is greater than he’ (Matt. 11:11). How is it that John was considered the greatest of prophets?
"First. He was entrusted with the important mission of preparing the way before the face of the Lord. Whoever had such a trust committed to him before or since? No man.
"Secondly. He was entrusted with the important mission, and it was required at his hands, to baptize the Son of man.
"Thirdly. John, at that time, was the only administrator in the affairs of the kingdom there was then on earth, and holding the keys of power. The Jews had to obey his instructions or be damned, by their own law which he had given to Moses on the mount, and thereby magnified it and made honorable, instead of destroying it. The son of Zacharias wrested the keys, the kingdom, the power, the glory from the Jews, by the holy anointing and decree of heaven, and these three reasons constitute him the greatest born of a woman. ...
“Jesus was looked upon as having the least claim in God’s kingdom, and, seemingly, was the least entitled to their acceptance of him as a prophet; as if he had said, ’He that is considered the least among you is greater than John—that is I, myself.’ ” (Hist. of the Church, vol. 5, p. 260-1)
To this we may be permitted to add that, according to the D. & C. (Sec. 84:28) John was ordained, when eight days old, “unto this power, to overthrow the kingdom of the Jews,” as well as to prepare them for the coming of the Lord. What a tremendous power and authority were his! And he exercised them, too. For with him the Mosaic dispensation came to an end.