Or HaChaim on Exodus 19:22/אור החיים על שמות י״ט:כ״ב

1 וגם הכהנים הנגשים אל ה׳ יתקדשו, "And also the priests who approach G'd have to sanctify themselves, etc." Although the priests (the firstborn in the main) are closer to G'd than the people at large, being allowed to perform sacrificial service in sacred locations, they too have to undergo a special sanctification process prior to the revelation. The fact that they normally adhered to strict standards of purity was not enough in this instance. They had to consider themselves as no better than the people at large. The meaning of the word יתקדשו is similar to the meaning of the word ודשנו in Numbers 4,13 where the priests are described as removing the ashes from the altar. The priests too had to remove themselves from the Mountain.