Im not certain if Dr. Doom is capable of this, but if he were to lift Doomsday's soul or bind him in a crystal or something magically, wouldnt that be the end of Doomsday?
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No...he'd just evolve past that. He evolved past chronal energy without even dying in H/P. He doesn't even need to die to evolve. Its happened almost instantaneously before.
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Granted I dont know a ton about Doomsday, but how do you evolve past having your life essence removed? Plus if he bound magically, he wouldnt technically be dead, so his body would have no reason to evolve. Unless he can control this mentally or something? I dunno, I always found this part of him to be a really contrived and childish explanation.