And it's not even biblical. Not that it would matter if it was, since the argument would be circular. For instance, I could write a book containing the sentence, "This book represents the word of God, whole and entire," but the sentence alone wouldn't prove the inspiration of my writings.
But at the very least the doctrine of "The Bible alone" should be found in Scripture, but it's not. Sure, the Bible upholds the value of Scripture, but never Scripture alone.
According to II Timothy 3:14-17, what else besides "Scripture" did Paul say was beneficial or profitable for doctrine, correction, exhortation and instruction ...? What else? Anything else? Then it is Scripture alone or sola Scriptura or sola Scripture that is profitable for these things --- and nothing else.