The rationale behind permitting the meat slaughtered by a non-Muslim from the People of the Book, but not that of other unbelievers, is that Jews and Christians hold it unlawful to sacrifice to anyone besides Allah and to consume carrion, in accordance with what their prophets taught them. Other disbelievers, by contrast, slaughter in the name of idols and consider carrion permissible.

Condition Two: the tool. Ritual slaughter is valid with any sharp implement that swiftly lets the blood flow—whether iron, stone, or anything similar—except for a tooth or a claw. It is unlawful to slaughter with either of these, for the Prophet, peace and blessings be upon him, said: “Whatever causes the blood to flow, eat of it—except the tooth and the claw.” Agreed upon.

Imam Ibn al-Qayyim remarked, “This ḥadīth serves as a warning against slaughtering with bones, either because some bones are impure in themselves or because their use would render them impure for the believing jinn. The continuation of the report states, ‘Let me explain: as for the tooth, it is bone’—meaning that, being bone, it may not be used for slaughter. He also said, ‘And the claw is the blade of the Abyssinians,’ that is, the knife employed by the people of Abyssinia; hence slaughtering with it is likewise impermissible.”

Condition Three: severance of the windpipe, which is the airway; the esophagus, which carries food and drink; and one of the two jugular veins.

Shaykh al-Islām Ibn Taymiyyah said, “The esophagus, the windpipe, and the two jugular veins are to be cut, and the stronger view is that severing any three of these four suffices to make the animal lawful, whether that includes…"