Class of All Ordinals is Well-Ordered by Subset Relation/Proof 2
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Let $\On$ be the class of all ordinals.
- $\subseteq$ is an ordering on $\On$.
- If $A$ is a non-empty subclass of $\On$, then $A$ has a smallest element under the subset relation.
The result follows from $g$-Tower is Well-Ordered under Subset Relation.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 1$ Ordinal numbers: Theorem $1.3$