I call bullshit on this one. Mining would cease to exist however, if there is enough incentive for the mining operators to leave their machines running and process transactions in the network, there would still be some form of 'mining' though the reward would be the fees included in a block. All bitcoins wouldn't disappear; they would still exist in circulation as long as their owners have it with them. Try reading more about how mining works and maybe, just maybe, you'll stop spreading misinformation.

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As for bitcoins being antiquities, I doubt it will ever be used as such, though I can see it taking up a similar role like that of gold. If bitcoin proved to be successful and if everyone would be using it in the future, I don't see any reason why some hobbyists would just let it sit there, or why would they collect such since it only exists within the realms of the internet? If it's a failure, how would one store it if the network of computers that keep bitcoin alive don't exist?