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I pretty much feel the opposite way. If Bitcoin dies, those altcoins aren't going to survive either. No matter which alts stay and go, Bitcoin will always stay. As far as being 'declared dead', that's happened a hundred times since its inception.
i am thinking the same way. but i say it totally depends on the situation that might go down. for instance if bitcoin died due to a security issue or something wrong with the whole cryptocurrency idea (which is not gonna happen) then all of the altcoins would have died too. because people are not going to look for an alternative for a failed thing.
but if dies because of circumstances like a worthy competition like an altcoin which actually offers useful features (nothing found yet!) that particular altcoin can replace it.