Singleton of Empty Class is Transitive
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Example of Transitive Class
Let $\O$ denote the empty class.
Then the singleton $\set \O$ is transitive.
Proof
There is one element of $\set \O$, and that is $\O$.
This is a subclass of $\set \O$.
That is, $\set \O$ is transitive.
$\blacksquare$
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 10$ Some useful facts about transitivity