There’s very little proof behind this. It has been studied and while wages go up, prices tend to only go up slightly here or there or even stay stagnant. McDonalds was a good case where the minimum wage went up but the only substantial change to any menu prices was on the Big Mac.And the problem with continuously raising minimum wage is everything increases along with it. So in the end, it feels like you were making the same as before.
And as @ghostsarejerks said, prices will increase anyway regardless of the minimum wage increasing. It’s been happening for years that way.