Shabbos, Chapter 10, Mishnah 5. The Mishnah opens with the case of "HaMotzi kikar lechem" - a single person who carries out a loaf of bread on Shabbos is liable. This ruling is straightforward, and it is brought only for the sake of comparison with the ruling that follows it.
Two people who carried out one loaf:
If two people carried out a single loaf, they are exempt. The basis for this is the halachah that two people who perform a labor together are not liable; the labor must be performed by one individual.
An object that one person cannot carry out alone:
The Mishnah adds a qualification: what is the ruling regarding an object that one person cannot carry out by himself - it is too heavy, too awkward or too bulky - and two people carried it out? In such a case both are liable, since by its very definition this is something that requires two people. Rabbi Shimon disagrees: even though two people are needed in order to carry it out, any labor performed by two people, even when it requires two, carries no liability.
Food less than the minimum measure inside a vessel:
The measure for liability when carrying out food fit for human consumption is kigrogeres, the size of a dried fig. If someone carries out less than that measure of food inside a vessel, the vessel is subordinate to the food, since it is there only for the sake of the food. There is no liability for the food itself, because it does not amount to the required measure, and therefore he is exempt for the vessel as well - even though a vessel on its own is something one would be liable for carrying out. Since its role here is to be subordinate to the food, and there is no liability for the food, there is no liability for the vessel either.
"HaChai nosei es atzmo":
There is a concept of "a living being carries itself": a living person, and according to many opinions animals as well, shift their weight and change their center of gravity while being carried, and therefore they are considered as carrying themselves. This is not genuine carrying of a burden with regard to Shabbos, and by Torah law there is no liability for carrying out a living person on Shabbos.
Accordingly, one who carries out a living person on a bed - the bed is subordinate to him, and is nothing more than the means by which he is carried. Just as there is no liability for carrying out the living person, so too there is no liability for the bed, since the bed is subordinate to him.
One who carries out a corpse on a bed:
However, one who carries out a dead body on a bed - here the principle of "a living being carries itself" does not apply. The corpse does not shift its center of gravity and does not assist the one carrying it in the act of carrying, and therefore he is liable for carrying out the corpse on Shabbos, and he is liable for the bed as well.
An olive's worth of a corpse, an olive's worth of a neveilah, and a lentil's worth of a sheretz:
The Mishnah continues: "V'chein k'zayis min hameis, uch'zayis min haneveilah, v'ka'adashah min hasheretz". These are:
K'zayis min hameis - an olive's worth of a corpse, which carries tumah.
K'zayis min haneveilah - an olive's worth of an animal that was not slaughtered properly, which also carries tumah.
Ka'adashah min hasheretz - a piece the size of a lentil from one of the eight creeping creatures listed in Parshas Shemini, which also carries tumah.
One who carries out any of these items on Shabbos is liable.
A labor not needed for its own sake:
But we must ask: why is he carrying them out? Presumably, in order to remove the tumah from his house. The question is whether that reason is sufficient to create liability on Shabbos. This question brings us to the topic of "a labor needed for its own sake" and "a labor not needed for its own sake": according to some opinions, a labor creates liability only when it is performed for the same purposes for which it served in the Mishkan. Carrying in the Mishkan was done in order to move an object from place to place, because the object was needed in the place to which it was brought.
Here, by contrast, one does not carry the corpse, the neveilah or the sheretz because it is needed outside, but because it is not wanted inside; if it were to disappear on its own, that would be just as good.
The Tanna Kamma in our Mishnah represents the opinion of Rabbi Yehudah, who holds that even a labor not needed for its own sake creates liability. Even though the labor is not being performed for the same purposes as in the Mishkan, since the person intends to perform the labor itself - only that he is not doing it in order to get the object outside but because he does not want it inside - he is liable.
It emerges that one who carries out on Shabbos an olive's worth of a corpse, an olive's worth of a neveilah or a lentil's worth of a sheretz is liable according to the Tanna Kamma, who is Rabbi Yehudah. "V'Rabbi Shimon poter" - Rabbi Shimon disagrees and holds that a labor not needed for its own sake, meaning a labor not performed for the purposes for which it was done in the Mishkan, carries no liability. Therefore in our case, where there is no desire for the impure object to be outside but only that it not be inside, he is exempt.