What you are saying basically is that inflation will cancel out all effects of the minimum income.
You are forgetting that the minimum income does not have the same relative impact on all incomes because people earn different amounts of money.
If the minimum income is 1000 Euro a month, and if everybody earned 10000 Euro a month, then yes, we would see a 10% income increase for everybody and a subsequent 10% inflation.
But some people earn only 2000 Euro a month, and others earn 20000. That means that for some, it is a 50% raise in income, and for others it is 5%. The inflation will lie somewhere in between - more than 5% but less than 50%.
In effect, the minimum income decreases the income gap. It lowers the income of the rich via inflation and it increases the effective income of the poor by raising their nominal income above the inflation rate.