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With reference to John Paul II saying eternal life is contingent upon union with God, there's this:

John 17:3
Now this is eternal life, that they should know you, the only true God, and the one whom you sent, Jesus Christ.

And this:

John 3:14b- 16
"the Son of Man be lifted up,
that everyone who believes in him may have eternal life.
For God so loved the world that he gave his only Son,
so that everyone who believes in him might not perish
but might have eternal life."

I think the difficulty comes in assuming that those who have "eternal life" are the only ones who have "eternal existence." It seems the damned as well have an eternal existence, but in so degraded a horror-state that Scripture will not say that what they possess is "life."

It is untrue to extrapolate from JPII a conclusion that he did not believe in Hell. In "Crossing the Threshold of Hope, Pope John Paul II said, "The words of Christ are unequivocal. In Matthew’s Gospel he speaks clearly of those who will go to eternal punishment." (cf. Matt. 25:46)