In one of the topics I read "If bitcoin will reach $10.000, fiat currency has become worthless"
Do you agree with this statement?
No. First of all because the value of fiat money don't depend from the value of bitcoin but from the other factors which have nothing to do with bitcoin.
Second because every fiat currency have an owner, mean "something" or "someone" which take care about that. This owner is every State of every country which has "order" the put of every currency in circulation and has given their the value these have. Everything made through an Authority with strong independence (mean very hard to interfere on its aim - take care and manage the currency of that country).
Third because bitcoin cannot replace (at least as it is) never the fiat currency in everything. So even if the world will prefer to use bitcoin and this will make worthless the fiat currency, cannot do this because bitcoin cannot be used out of the internet. Here exist an option that can be chooses and can realize the use of bitcoin even out of internet - and are credit and debit cards - but this option remain to be verified. There are already such options in the market but not very attractive and not with much spread. Anyhow potentially this choice can be used.
Fourth. Not only that value given above for bitcoin but even a new one ten time more of that, have nothing to do with the making worthless the fiat currency, is even the fact that the amount of bitcoin in circulation is not and will be not able to cover all the continuously in increase needs of the world for money (accepting that the being worthless of all currencies will made them only paper for toilet). Bitcoin is limited and even if goes down with its use (so are used milisatoshi, minisatoshi or even simple satoshi) yet are not enough to the needs. To not forget that every year the increase of economies need new money in circulation. And this increase will always be much more than the capacity of bitcoin to fulfill that.
The last one is that no one country may allow that such thing happen. They cannot leave their currency to become worthless and have as currency one such which, at least, is not owned by those and as such cannot be used to realize their monetary policies as these want. Not only this but and not owned currency put in risk even the stability of the country which use one such. Everyone can use it to destabilize the economy of that country.