It isn't proven, contrary to the responses in this thread. Bitcoin's prices has largely been on the uptick since its inception mainly due to the adoption by the major players and/or governments. It would be incorrect to formulate an opinion solely because of that. Conversely, Bitcoin has largely been influenced by the general market trends; downtrend in the market typically results in lower crypto prices, and vice versa.
However, Bitcoin holds the specific characteristic which is a good hedge against inflation. Assuming that the demand remains constant, the decreasing supply would in theory result in Bitcoin being more valuable.
As I understand it, any asset that can increase in value over time can be considered an inflation hedge. Tech stocks are also seen as an inflation hedge to some extent. So bitcoin can be seen as an asset that protects us from inflation, but it is not an good inflation hedge and is not yet a safe haven asset in the traditional sense (gold).
Indeed, to become a good asset hedge against inflation, bitcoin needs to prove its potential and capabilities. It would be biased to jump to the conclusion that bitcoin is a safe asset to hedge against inflation just because the government has recognized it as legal. It needs to show people it can do what gold did.