"Testament"="covenant"

   1. Jesus redeems mankind by His blood.
"Hebrews 9:12"

Hebrews 9:12 12 Not with the blood of goats and calves, but with His own blood He entered the Most Holy Place once for all, having obtained eternal redemption.

   2. Jesus died for all sins committed under the Old and New Covenant.
"Hebrews 9:15"

Hebrews 9:15 15 And for this cause He is the mediator of the New Testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. KJV

   3. The New Covenant came into effect after Christ's death on the cross.
"Hebrews 9:17"

Hebrews 9:17 17 For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth. KJV

  5. Those saved before the cross were not under the rules of the New Testament of Jesus.
Luke 23:"

Luke 23:42, 43 And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.

  5. The first testament is "old"
Hebrews 8:13"

Hebrews 8:13 In that he saith, A new covenant, he hath made the first old. KJV