Indeed, fasting is not affected as long as we are sure nothing of the toothpaste remnants is swallowed. In addition, there is nothing wrong that we swallow our saliva after using the toothbrush. With this in mind, we do advise to rinse water into the mouth several times after using the toothbrush in order to make sure that all the remnants of the toothpaste are not there in the mouth. This will help remain in the safe side regarding your fasting.