Parashas Acharei Mos · Passuk 16:23
Chabad.org — English translation + Rashi
Torah Temima points to Yoma 31b.
English: “And he shall remove… and wash… and put on…” — the Torah equates removal with donning: just as when he dons the garments he sanctifies (washes hands and feet) while clothed, so too when he removes them he sanctifies while still clothed.
Hekesh (comparison) between peishitah and levishah.
Kiddush yadayim v’raglayim is performed while still wearing the garments both when putting them on and when taking them off.