Does swallowing saliva mixed with a small amount of blood invalidate prayer, by analogy with its not invalidating the fast during Ramadan according to the Hanafis?

If blood comes out from between the teeth and a fasting person swallows it, then if the saliva is predominant and he does not taste it, his fast is not invalidated. Otherwise, it is invalidated. Prayer is not invalidated by a small amount of blood coming out of the mouth if it does not fill the mouth, and ablution is not nullified by it unless the blood predominates over the saliva or is equal to it.