The Gemara in Shabbos 117b derives from a pasuk in this week’s parshah regarding the falling of the mon that we are obligated to eat three seudos on Shabbos. The Gemara there also brings from another pasuk in this week’s parshah that at each seudah we are obligated to break bread on two loaves. This is known as lechem mishneh.
Generally, women are exempt from mitzvos assei she’hazman grama (time-sensitive mitzvos). Although the obligation to eat three seudos and lechem mishneh are mitzvos assei she’hazman grama, nonetheless the Ran on that Gemara (44 dafei haRiff) quotes Rabbeinu Tam, who says that women are obligated in both of these mitzvos as a result of the rule of af ha’im hayu b’osah haneis – they too were involved in the miracle. This halacha is the reason that women are obligated in the mitzvos of Chanukah candles, drinking the four cups of wine at the seder, and hearing the Megillah on Purim.
The Ran there says that it is not necessary to obligate women as a result of the rule of af ha’im hayu b’osah haneis because the Gemara in Brachos 20b derives from a hekish that regarding all obligations of Shabbos women are obligated just like men. As a result of this hekish women are obligated in the mitzvah of kiddush on Shabbos. (Women are obligated in the lo sasseis of Shabbos regardless of any hekish or drashos, for they are always obligated in every lo sassei.)
The Kapos Temarim, in Sukkah 38a, defends Rabbeinu Tam’s opinion and explains that it is necessary to draw from the rule of af ha’im hayu b’osah haneis that women are obligated in eating three seudos with lechem mishneh. He explains that the hekish that the Gemara in Brachos makes only regards obligating women in kiddush, not on all other obligations on Shabbos.
I believe that not all agree with the opinion of the Ran and Rabbeinu Tam that the rule of af ha’eim hayu b’osah haneis applies to the obligation to eat three seudos with lechem mishneh.
Tosafos in numerous places inquires why women are not obligated in several different mitzvos as a result of the rule of af ha’eim hayu b’osah haneis. In Megillah 4a, for example, Tosafos asks why it was necessary for the Gemara to find a drasha to obligate women in eating matzah on Pesach, when they could have been included in the mitzvah as a result of the rule of af ha’eim hayu b’osah haneis? Tosafos in Pesachim (108b) asks why women are exempt from the mitzvah of sukkah when the pasuk in Vayikra 23:43 says that we have the mitzvah of sukkah as a result of Hashem’s miracle of making sukkos for us in the desert. Thus, they should be obligated as a result of the same rule of af ha’eim hayu b’osah haneis.
The Chasam Sofer (teshuvos Orach Chaim 185) asks why women are not obligated in the mitzvah of tefillin. The pasuk in Shemos 13:9 says that we wear tefillin because Hashem took us out of Mitzrayim. Based on that, women should be obligated in the mitzvah of tefillin as a result of af ha’eim hayu b’osah haneis.
The Sefer Harirai Kedem quotes the following answer from Rav Moshe Soloveitchik to these questuions. He explains that there is a difference between a mitzvah whose essence is to publicize the miracle and a mitzvah that serves as a reminder to a miracle. There are only three times when the Gemara says that women are obligated in mitzvos as a result of the rule of af ha’eim hayu b’osah haneis: lighting candles on Chanukah, reading the Megillah on Purim, and drinking four cups of wine on Pesach. The essence of all three of these mitzvos is to publicize the miracle associated with them. The mitzvos of sukkah, matzah and tefillin are all connected to miracles; however, they are merely a remembrance of the miracles. The essence of these mitzvos is not to publicize the miracle (pirsumei nissa).
The only time that the rule of af ha’eim hayu b’osah haneis can obligate one in a mitzvah is when the essence of the mitzvah is to publicize the miracle. Since the essence of the mitzvos of sukkah, matzah and tefillin are not pirsumei nissa, the rule of af ha’eim hayu b’osah haness cannot obligate women in those mitzvos.
The mitzvah of eating three seudos with lechem mishneh is not in essence to publicize the miracle of the mon. rather the mitzvah serves as a rememberance of the the miracle. Based on Rav Moshe Soloveitchik’s explanation, the rule of af ha’eim hayu b’osah haneis would not apply here.