I want to prove that the class of all sets $\mathbb{S}=\{x \mid x=x \}$ is a stage (p. 15) (and then that it is a limit thus that it is the successor of another stage).
One way to do it is to proof that $\mathbb{S} = acc(H(\mathbb{S}))$
where $H(S)$ is the history (p. 15) of a class $S$ and
$ acc(A) := \{x \mid \exists y \in A; \ x \in y \lor x \subseteq y \}.$
I'm trying to figure out what the history of $\mathbb{S}$. Any hints on that? Is that even a good approach to proof that $\mathbb{S}$ is a stage?