Weeping/mourning/sadness becomes joy through Jesus Christ

Here is a very short note showing an intriguing connection between the New Testament and the Book of Mormon.

Here are Christ's words from John 16:

20 Verily, verily, I say unto you, That ye shall weep and lament, but the world shall rejoice: and ye shall be sorrowful, but your sorrow shall be turned into joy.

And here are Mormon's words from 3 Nephi 10:

10 And the earth did cleave together again, that it stood; and the mourning, and the weeping, and the wailing of the people who were spared alive did cease; and their mourning was turned into joy, and their lamentations into the praise and thanksgiving unto the Lord Jesus Christ, their Redeemer.

This is really interesting to me. I can't help but assume that but accounts are based off of an earlier scripture. I looked for some possible candidates, though we may not have it in our current scriptures. Here are some possibilities:

5 For his anger endureth but a moment; in his favour is life: weeping may endure for a night, but joy cometh in the morning. (Psalm 30)

2 To proclaim the acceptable year of the Lord, and the day of vengeance of our God; to comfort all that mourn;

3 To appoint unto them that mourn in Zion, to give unto them beauty for ashes, the oil of joy for mourning, the garment of praise for the spirit of heaviness; that they might be called trees of righteousness, the planting of the Lord, that he might be glorified. (Isaiah 61) 

13 Then shall the virgin rejoice in the dance, both young men and old together: for I will turn their mourning into joy, and will comfort them, and make them rejoice from their sorrow. (Jeremiah 31)