Will Ethereum/Altcoins Be Valuable Or Relevant without Bitcoin?

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I happen to be in a group that has to be with Bitcoin or cryptocurrencies in general. There was an argument recently, for and against, about the fact that non-existence (if possible) of Bitcoin would render or make Ethereum (and other altcoins) useless.
The stronger argument which is for Bitcoin had it that if it happens that there was no Bitcoin again, other coins/tokens would also stop having values. They might justify this because bearish trend in Bitcoin affects almost all other, and for other related reasons.

In my own knowing, I knew that Bitcoin came on the scene the first, and that the idea of it inspired Ethereum second, which gave platform for many Ethereum-based tokens, and there are also other platform-based tokens also like Wave, Stellar, etc
Could all of these starting from Ethereum still exit or useful if Bitcoin wouldn't be any more?
The answer to me is in affirmative, but can anyone lecture on why not?
Insightful answers please.