誰でも (anyone/ everyone/ everybody/ anybody)
誰も〜ない (no one /none /nobody )
誰も is always used with ない as a negative form of 誰でも, so 誰も is just only a part of it.
Ex)
None of my family can drive a car. (= 家族の誰も車を運転できない。)
Anyone of my family can drive a car. (= 家族の誰でも車を運転できる。)