Empty Class is Supercomplete
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Hence $\O$ is transitive by definition.
Hence $\O$ is swelled by definition.
The result follows by definition of supercomplete.
- 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: $\S 3$ Axiom of the empty set: Note $2$.