When bitcoin price hits 10,000$, Perhaps we will not use traditional currency (cash).
Untill that time, we will be using smart devices to pay everything with bitcoin.
Even if bitcoin reaches a new ATH each month, fiat will still has value, it is not affected by bitcoins price increase. Fiat's value will only be gone when no one uses it and
the country that owns it is not reproducing it anymore and put into circulation. That's the only time that fiat's value will start to drop.
It can also be the other way round. The country that owns the currency might be printing too much of it, and the circulation gets overwhelmed with an excessive amount of money leading to hyperinflation. This is what happened in Zimbabwe and can potentially happen to any fiat money in any country. If something like that happens to American dollar or Chinese yuan, the Bitcoin price will soar, and it will be an obvious outcome of the depreciation of any of these currencies.