Halakhah su Besah 1:13

For example, the Mishnah (Beitzah 1:5) records that Beit Shamai do not permit carrying a child, lulav, or Sefer Torah in a public domain on Yom Tov, while Beit Hillel do permit such carrying. The Gemara (Beitzah 12a) explains that Beit Hillel believes that “mitoch shehutrah hotza’ah letzorech. hutrah nami shelo letzorech”, “Given that the Torah permits carrying for the sake of food preparation, it permits carrying for any Yom Tov need,” while Beit Shamai rejects this expansion. This concept is commonly referred to as “mitoch” and applies to all melachot that are permitted on Yom Tov. The Halachah follows the opinion of Beit Hillel (Shulchan Aruch O.C. 518:1).