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The takanah of Rabbi Yochanan ben Zakai was made as a lo plug, no differentiation whether there was an eruv or not. Also, it is not just a matter of carrying with no eruv.this is discussed in Not Shaking the Lulav on Shabbat. As Rashi explains, if communities with an eruv start bringing the lulav to shul, they would be violating the takanah of Rabbi Yochanan ...


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An eruv is no better than one's own house. When Rav Yochanan ben Zakkai made the takana, he could have made it that everyone should take the lulav in their house before coming to shul. But we see that he was concerned that there might be one person who needed help, and would thus leave his house to ask for help in a forbidden way. It's a far-fetched concern,...


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