Is it permissible to use toothpaste and soap that contain pork fat?

Pork is impure and its consumption is strictly forbidden. This is indicated by the Almighty's saying: "Forbidden to you are carrion, blood, and the flesh of swine" and His saying: "Say, 'I find not in what has been revealed to me anything forbidden to be eaten by an eater except that it be carrion or blood poured forth or the flesh of swine—for indeed, that is an impurity.'" It was also narrated from the Prophet, peace and blessings be upon him: "Whoever plays with backgammon, it is as if he has dipped his hand in the flesh and blood of a pig." The prohibition includes all parts of the pig, as stated in the hadith: "Indeed, Allah has forbidden the sale of intoxicants, carrion, swine, and idols." Based on this, if it is confirmed that toothpaste or soap contains pork fat or any substance derived from it, then it is impure, and it is not permissible to use or sell it. However, this must be verified, and one should not rely on rumors.