A reduction to the absurd reveals that the quantity of money is relevant to the price level. Try to run the economy with one dollar changing hands and, since it can't change hands fast enough, that single dollar is priceless. Try having an absurd (approach infinity) number of dollars and, even if circulation speed is near zero, dollars will have near zero value.

Naturally, it is monetary mass coupled with circulation speed. If you change the monetary mass and no other economic variable, within the tolerance envelope, circulation speed will adapt and price levels won't budge. Exceed tolerance levels, and you will influence price levels.

You saw this applied in practice recently. Quantitative easing is a correction using monetary mass to an abnormal reduction in circulation speed (via reduced lending).