Though Nietzsche rarely spoke of Hegel, and when he did he treated him more as a cultural force than a source of valid ideas, it is clear to me, based on my own experience of reading him, that Nietzsche thought dialectically, in the Hegelian sense.
It is undeniable that the Birth of Tragedy has an explicitly dialectical structure, and Nietzsche’s later disavowals of the work centered more on their treatment of Wagner than in the Apollinian-Dionysian-tragic dialectic at the center of the book. Actually, that structure is the key to understanding the apparent self-contradictions that pervade the rest of his work.
Once you start looking at Nietzsche through a dialectical lens, sooner or later you are bound to wonder if the concept of antichrist isn’t primarily an antithetical term of a larger dialectic.
Maybe the form thesis – antithesis – synthesis is a distortion of what really goes on in dialectic.
Maybe it’s thesis – antithesis – synesis.
The synesis is not itself a thesis, but a perspective of understanding that produces theses, perceptions, actions — in short, a whole lifeworld.