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It is forbidden to do [certain] Melachos on Chol ha'Mo'ed. (1)
Chol ha'Mo'ed is referred to by the Torah as "Mikra Kodesh." Consequently, a Kal va'Chomer teaches that Melachah is prohibited on Chol ha'Mo'ed.
The Torah empowered the Chachamim with the authority to decide which Melachos are prohibited on Chol ha'Mo'ed and which are permitted.
When the make-up day for the Korbanos of Shavuos is Sunday, fasting and eulogizing is permitted, in order not to give any credibility to the Tzedukim who say that Shavuos must always fall on Sunday. (2)
Terumah and Bikurim share many of the same laws. (3)
Rebbi Meir: One does not need to wash his hands prior to eating Ma'aser Sheni. Chachamim: One must was his hands. (4)
One does not need to wash his hands prior to eating Chulin unless he is eating bread. (5)
A BIT MORE
1. According to some Tana'im, the prohibition of Melachah on Chol ha'Mo'ed is derive from the verse. According to Rebbi Yonasan, it is derived from a Kal va'Chomer.
2. If the make-up day for the Korbanos of Shavuos is any day other than Sunday, it is prohibited to fast or eulogize on that day.
3. A non-Kohen who knowingly eats Terumah or Bikurim is punished with Misah. If he eats it unintentionally, he must pay the principle plus a fifth (of the ensuing total). Both are the property of the Kohen, both are nullified in a mixture only one part in a hundred, and both require Netilas Yadayim and He'erev Shemesh.
4. Everyone agrees that there is no need to wash hands prior to touching Ma'aser Sheni.
5. One who washes his hands prior to eating fruit is regarded as haughty.
The Gemara says that Rebbi Tarfon did not allow eulogizing on the Yom Tavo'ach. Even though the Mishnah permits fasting and eulogizing on the Yom Tavo'ach, that applies only when the Yom Tavo'ach is on Sunday so as not to give credibility to the Tzedukim who say that Shavuos is always on Sunday. Rebbi Tarfon did not allow them to eulogize on that day because fasting and eulogizing are prohibited on a day on which one brings a Korban. Even though Rebbi Tarfon lived after the destruction of the Beis ha'Mikdash and no Korbanos were being brought on the Yom Tavo'ach, he prohibited fasting and eulogizing since the Korbanos of Shavuos would have been brought on this day had the Beis ha'Mikdash been standing. (Mishneh l'Melech)
Some Melachos are permitted on Chol ha'Mo'ed, while others are prohibited. It depends on how essential the Chachamim deemed the Melachah to be. (Shulchan Aruch OC 530:1)
A person should be extremely careful not to be more lenient than is allowed according to Halachah, because the Chachamim say that one who disgraces the Mo'ados (by doing Melachah on Chol ha'Mo'ed, Rashi) is tantamount to one who worships Avodah Zarah. (Mishnah Berurah)
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