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.
But the value of the fiat will decrease faster when more people use the bitcoin.