Some categories of melacha are permitted on chol hamoed. Are there any categories of melacha that are prohibited on chol hamoed at the biblical level (d'oraissa)?
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That depends on how we Pasken.
It seems from the Gemera in Chagiga 18a that it's a Biblical prohibition to do [certain] work on Chol HaMo'ed. The Gamara brings about half a dozen verses to prove that.
But Rashi and Tosafot already argue as to whether it's really Biblical or Rabbinic [with a Asmachta (hint) on the Torah].