Subclass of Well-Ordered Class is Well-Ordered
Let $V$ be a basic universe.
Let $\RR \subseteq V \times V$ be a relation.
Let $B$ be a subclass of $A$.
Then $B$ is also well-ordered under $\RR$.
First suppose $B$ is the empty class.
Hence the result by definition of well-ordered class.
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $4$: Superinduction, Well Ordering and Choice: Part $\text I$ -- Superinduction and Well Ordering: $\S 1$ Introduction to well ordering: Proposition $1.1$