BT Yom 42a(23) :ולאו כל דכן הוא, קדשי בדק הבית בעו כהנה, קדשי מזבח מיבעיא‏ : is it not an argument a fortiori? if a priest is needed for the sanctification of the whole temple, surely it is needed just for the altar
See the entire entry for kl@dkn adv. how much more/less