Is the hide of an animal whose flesh is not lawful to eat rendered impure (najis) after being slaughtered?

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Abu Hanifa and Malik hold that the hide becomes pure (tahir) because the Prophet (peace be upon him) stated, "Tanning of the leather is its lawful slaughter (dhabihah)," implying that tanning is analogous to slaughter. They argue that since the weaker analogy (tanning) purifies, the stronger analogy (slaughter) must also purify. Furthermore, tanning removes impurity after its occurrence, while slaughter prevents it; prevention is considered stronger than removal. They also cite the Prophet's prohibition against using the skins of beasts of prey for sitting or riding, which applies regardless of whether the animal was ritually slaughtered or not. They further argue that since slaughter does not purify the flesh, it does not purify the hide, similar to the slaughter performed by a Magian (Zoroastrian).