As an accounting identity you have that PQ=MV, where P is the price level, Q is the real economy (goods produced), M is the money supply and V is the velocity of money (if the economy has one $100 bill, which gets spent twice, then M is 100 and V is 2).
This has to be true. Dividing by Q gets us that the price level P equals MV/Q, which also means that inflation (change in P) depends on the change in M, V and Q. In the short run prices are sticky, so Q is relevant. Increased wages do not impact the money supply, so inflation would have to be because of an increased velocity of money (possible) or lower GDP (possible). In the long run money is neutral, meaning that it doesn't affect the real economy, so we can disregard Q; changes in the price level depends on changes in the money supply and the velocity of money. Again, higher wages do not impact the money supply so the velocity of money is the only avenue. The Quantity Theory of Money is the introductory thing to read about if you want to google. Here they drop the V as well, but you don't have to buy that to get the gist of it.
This isn't even touching on employers having market power (meaning that higher wages wouldn't necessarily depress production, it might increase it, it might do nothing, it might depress it but not proportional to the wage hike), or changes in the exchange rate.
Of course, a way to view GDP is the sum of all incomes, so in that sense it's impossible to increase income without changing the price level, but this is pedantic because this is all sources of income instead of wages, and in addition when we talk about how wages haven't kept up with inflation we're talking about the median wage or below, not even all wages.