Latest update: April 25th, 2013
Rabbi Akiva Eiger quotes the ruling of the Rush in Shabbos 2:12: the more frequent mitzvah will eliminate another mitzvah if all else is equal. The Rush proves this from the Gemara in Shabbos that discusses which mitzvah would eliminate the other – Shabbos candles or Chanukah candles. The Gemara concludes that Chanukah candles should eliminate Shabbos candles because, as previously mentioned, it accomplishes pirsumei nisa. From the fact that the Gemara discussed this question and raised the possibility that the more frequent mitzvah would eliminate the less frequent one shows us that if not for the fact that Chanukah candles accomplish pirsumei nisa, the more frequent mitzvah would eliminate the less frequent mitzvah.
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