Pesachim, Chapter 6, Mishnah 2. This mishnah continues the previous one, in which the first tanna and Rabbi Eliezer disagreed about whether certain acts may be performed on Shabbos for the sake of bringing the korban Pesach - acts that could have been done before Shabbos but were not, and which are forbidden only rabbinically. The first tanna holds that they may not be done, since they could have been done on erev Shabbos; Rabbi Eliezer holds that they override Shabbos. In our mishnah Rabbi Eliezer explains his reasoning.
Rabbi Eliezer's argument - a kal vachomer:
Rabbi Eliezer said: "Vahalo din hu" - this follows by a kal vachomer. "Mah im shechitah shehi mishum melachah dochah es haShabbos" - slaughtering is a melachah forbidden by Torah law, and nevertheless it overrides Shabbos for the sake of the korban Pesach. "Eilu shehen mishum shevus" - the acts listed in the previous mishnah: bringing the animal from outside the techum, carrying it in Yerushalayim, and cutting off a wart in a manner forbidden rabbinically, are forbidden only by rabbinic law. "Lo yidchu es haShabbos?" - all the more so they should override Shabbos.
Rabbi Yehoshua's response - "Yom Tov yochiach":
Rabbi Yehoshua answered him: "Yom Tov yochiach" - the laws of Yom Tov prove the opposite. "Shehitir bah mishum melachah" - on Yom Tov a full melachah is permitted, for one may cook for the sake of food. "Ve'asar bah mishum shevus" - and nevertheless rabbinic prohibitions remain forbidden on it, such as bringing food or an animal from outside the techum, even though it is done for the sake of eating. We see, then, that at times a Torah melachah is permitted while a rabbinic prohibition remains in force, because it could have been done on erev Yom Tov.
"Mah rayah reshus lemitzvah?":
Rabbi Eliezer replied: "Mah zeh Yehoshua?" - Rabbi Yehoshua was his contemporary, and therefore he did not address him with the title "Rabbi." "Mah rayah reshus lemitzvah?" - eating on Yom Tov is merely optional, something a person is permitted to do but is under no obligation to do, and no proof may be brought from it to a mitzvah such as offering the korban Pesach. In Rabbi Eliezer's view, for the sake of fulfilling the mitzvah of the korban Pesach these rabbinic prohibitions should be permitted. The Gemara explains that Rabbi Yehoshua held that the joy of Yom Tov, the eating and the pleasure involved in it, is itself a mitzvah.
Rabbi Akiva's proof from sprinkling:
At this point Rabbi Akiva entered the debate, even though he was a student of both Rabbi Yehoshua and Rabbi Eliezer, and answered Rabbi Eliezer from the law of sprinkling: one who became tamei and needed to have the waters of the parah adumah sprinkled upon him on erev Pesach, so that he would become tahor and be able to eat the korban Pesach - this is a mitzvah, and nevertheless the Sages said that he is not sprinkled upon on Shabbos because of a rabbinic prohibition. Rashi explains that sprinkling is considered like repairing: it repairs the person and makes him fit, since beforehand he was not fit, and its prohibition is rabbinic or because of a decree. The Gemara offers another reason: a decree lest he carry the waters of the chatas in the public domain.
It emerges that sprinkling is a mitzvah, and its prohibition is only rabbinic, and nevertheless it does not override Shabbos. If so, there is no reason to wonder about the other rabbinic prohibitions that do not override Shabbos, even though they are done for the sake of the mitzvah of bringing the korban Pesach.
Rabbi Eliezer's response and Rabbi Akiva's counter-argument:
Rabbi Eliezer answered: regarding sprinkling as well, the sprinkling of the waters of the chatas that purify a person, I have a question. If slaughtering, which is a Torah melachah, overrides Shabbos, then sprinkling, which is only rabbinic - all the more so should it override Shabbos. But in fact, as the Gemara explains, it was Rabbi Eliezer himself who had taught Rabbi Akiva that sprinkling does not override Shabbos, and he had forgotten this; in order to remind him, Rabbi Akiva put forward the opposite argument.
Rabbi Akiva said to him: perhaps the reverse is true - just as sprinkling, which is only rabbinic, does not override Shabbos, so too slaughtering, which is a Torah melachah, should not override Shabbos. Certainly this is not so, for one may indeed slaughter the korban Pesach on Shabbos; rather, Rabbi Akiva wished to remind his teacher, in a respectful manner, that he himself agrees that sprinkling is rabbinically forbidden even on Shabbos.
"Akiva, akarta mah shekasuv baTorah":
Rabbi Eliezer did not grasp his intent and wondered: "Akiva, akarta mah shekasuv baTorah" - for the Torah states "bein ha'arbayim bemo'ado", that the offering is brought in the afternoon at its proper time, and from that word we learn "whether on a weekday or on Shabbos" - that the korban Pesach is brought both on a weekday and on Shabbos. We see, then, that slaughtering overrides Shabbos.
Rabbi Akiva said to him: "Havei li mo'ed le'eilu kemo'ed lishchitah" - bring me a source teaching that these rabbinic prohibitions are to be set aside, just as the Torah said that Shabbos is set aside for the sake of slaughtering. Regarding slaughtering it is stated explicitly, because it cannot be done other than on Shabbos; whereas these acts could have been done on erev Shabbos.
Rabbi Akiva's principle:
On this basis Rabbi Akiva established a principle: "Kol melachah she'efshar la'asosah me'erev Shabbos einah dochah es haShabbos, ushchitah she'i efshar la'asosah me'erev Shabbos dochah es haShabbos" - every act that could have been done on erev Shabbos does not override Shabbos, while slaughtering, which cannot be done on erev Shabbos, does override Shabbos. The word "melachah" here appears to include rabbinic prohibitions as well:
Any act that could have been done on erev Shabbos - does not override Shabbos, even though the mitzvah itself is performed on Shabbos.
Slaughtering, which cannot be done on erev Shabbos - and must necessarily be done on Shabbos itself, overrides Shabbos.
In summary: in this mishnah Rabbi Eliezer supported his position with a kal vachomer from slaughtering, which is a Torah melachah and overrides Shabbos. Rabbi Yehoshua rejected this from the laws of Yom Tov, on which a melachah is permitted while a shevus remains forbidden, and Rabbi Eliezer responded that no proof may be brought from something optional to a mitzvah. Rabbi Akiva proved his point from sprinkling, which is a mitzvah and whose prohibition is rabbinic, and which nevertheless does not override Shabbos, and in a respectful manner he reminded Rabbi Eliezer of his own ruling. In the end the principle was established: whatever can be done on erev Shabbos does not override Shabbos, and only what cannot be done other than on Shabbos - such as slaughtering the Pesach - overrides it.