Is it permissible to use toothpaste that contains sorbitol, knowing that it is an alcoholic substance, and it is impossible to prevent some of it from entering the alimentary canal?

Alcohol is an intoxicant, and no type of it is permissible to use if it mixes with something before its transformation. It is considered impure and impermissible to use. However, if it undergoes a complete transformation into a non-intoxicating substance before mixing, then it becomes pure due to the removal of its intoxicating quality. Therefore, if it is highly probable that the toothpaste contains alcohol, it is not permissible to use it unless it is known that the alcohol transformed into a non-intoxicating substance before it was mixed.