Is the fast of one who expels something from his throat or from between his teeth and spits it out valid?

This fast is valid as long as its observer did not swallow anything that came out of their stomach after it was possible to expel it. If they swallowed it after it was possible to expel it, their fast is broken. However, if it did not reach the mouth such that it could be spat out, or if it was a small amount that could not be expelled and they swallowed it, the fast is not broken by that.