הלכה על ביצה 2:5

The Mishnah (Beitzah 2:5) presents a debate between Beit Hillel and Beit Shamai as to whether one may heat water for washing one’s hands, face, and feet on Yom Tov. Predictably, Beit Shamai forbids this due to its rejection of the idea of mitoch, while Beit Hillel permits this activity on the basis of mitoch,