Little more complicated then that, but I think it's safe to say that as the bitcoin price goes up more often then not the difficulty of mining bitcoin will also be going up. There may be some changes with this due to the fact of splitting of the amount of Bitcoins that are given as the fee, but you're correct in a general sense.
You could always compare this (
https://www.coindesk.com/data/bitcoin-mining-difficulty-time/) and the price of Bitcoin (you can find this anywhere, probably on the same link)