Yeah. The sins of the world were in the cup, but blood had to be spilled for our sins. John 18:11. I can see your simple meaning, but there is also a deeper meaning as well.
I agree that without the shedding of blood there is no remission of sins.
Here is a chronological break down:
#1. Jesus (Who is God and the spotless Lamb) took on our sins in the Garden.
#2. Jesus was whipped and beaten in our place (Isaiah says he was wounded for our transgressions and crushed for our iniquities and by his stripes (whip marks) we are healed).
#3. God the Father laid the full Judgment upon the Son on the cross. It is why Jesus felt a separation from the Father (even though He was not separated from Him).
#4. Jesus was crucified (shedding His blood) upon the cross and paid the penalty for our sins.
#5. Jesus was in the grave three days and three nights (72 hours exactly).
#6. Jesus rose from the grave.
#7. After Jesus told Mary not to touch him, Jesus ascended to the Father (And became our Heavenly High Priest and mediator between God the Father and man) so as to offer us the free gift of salvation. This gift was to be Himself. For Jesus intercedes on our behalf by what He has done for us.
#8. Jesus today can live inside of us and redeem us.
This is why the fruit of Christ will be evident in our lives and not evil or bad fruit. For Jesus is the source of our life who lives inside of us (See 1 John 5:12). Jesus works in our lives to overcome sin after we repented and accept Him as our Savior (See Romans 13:14).
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