No. Not at all. That is a huge unfounded logical leap. "Eternal death" is a mess, you mean eternal suffering or torment or whatever. "Eternal death" means the same as "death". It's like "blue" or "really blue".:doh:
The "life" in "eternal life" is not simply existence. So "eternal death" would not require "eternal life."
Yes, the "eternal life" given to the saved has a lot of baggage attached, and it is not simply existence. It's all good baggage and it's awesome. But "eternal life" still means "eternal life", and "death" is still the opposite. The opposite of eternal life is shown for the lost in all the passages that talk about "death" "destruction" "dying as beasts" "turning to ashes" "vanishing as smoke"... which you have not touched once in this conversation. I want to be right LH, I want you to blow me out of the water if I am wrong. Hit on those verses and show me where I missed. How do those verses not mean what they seem to say?
If that's what the Bible says then maybe someone will be able to provide the Scripture?
I have one for my side:
For Christ also suffered once for sins, the just for the unjust, that He might bring us to God, being put to death in the flesh but made alive by the Spirit, by whom also He went and preached to the spirits in prison,
-1 Peter 3:18-19
So, His flesh was dead but His Spirit remained, separated from the Father, while He preached to the spirits in prison.
Then there is this:
Therefore, being a prophet, and knowing that God had sworn with an oath to him that of the fruit of his body, according to the flesh, He would raise up the Christ to sit on his throne, he, foreseeing this, spoke concerning the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption.
-Acts 2:30-31
And also this:
Therefore He says:“When He ascended on high,(Now this, “He ascended”—what does it mean but that He also first descended into the lower parts of the earth? He who descended is also the One who ascended far above all the heavens, that He might fill all things.)
He led captivity captive,
And gave gifts to men.”
-Ephesians 4:8-10
Because Christ was resurrected it makes more sense to believe those in Hell will also one day be resurrected than to believe they will be annihilated.
The simple truth is I don't compare the details of how Jesus died to how the lost died. If I need to I'll go back and look at it. I liked the look of Timotheos'eses post and quoted it.