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According to the Torah, melacha isn't permitted on Yom Tov days except for what is needed for food. I read that certain laws, like carrying, don't apply on these days because they are loosened for food preparation... and if for food, then also for anything else that is needed for the holiday.

How is this leap derived, from 'food' to 'things needed for celebrating the day'?

What makes the question more interesting is that I think one couldn't take a different perspective of the halachic process for him or herself as an individual (and treat the day like Shabbos, except for preparing food) because it would interfere with lighting candles as the community is obliged to.

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Pretty much, the Hachamim received a tradition that some Melachot (לִישָׁה, אֲפִיָּה, שְׁחִיטָה וּבִשּׁוּל. וְהוֹצָאָה וְהַבְעָרָה ) are Mutar לְצֹרֶךְ אֹכֶל נֶפֶשׁ because they are included in the meaning of לְצֹרֶךְ אֹכֶל נֶפֶשׁ.(from the Kisur Shulhan Aruch). –  Hacham Gabriel Sep 1 '13 at 16:40
    
halachipedia.com/… footnote one gives the sources you might be asking for –  Danno Sep 1 '13 at 16:41
    
related judaism.stackexchange.com/q/20430/759 –  Double AA Sep 1 '13 at 20:29
    
The principle in play here is called "Mitoch" (מתוך). I don't know what kind of level explanation you are seeking, but a Google search for "mitoch yom tov" might prove fruitful. –  Double AA Sep 1 '13 at 20:31
    
Thanks, I did find some interesting things. But nothing to answer the question of why, when the Torah says that you can't work except what is needed to eat, that can possibly be more broadly applied to things not needed for food. –  Annelise Sep 2 '13 at 2:29

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