Empty Class is Transitive

Example of Transitive Class

The empty class is transitive.


Proof

Vacuously, every element of $\O$ is also a subclass of $\O$.

Hence $\O$ is transitive by definition.

$\blacksquare$


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
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