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We have the following indirect implication of form equivalence classes:

30 \(\Rightarrow\) 10 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
30 \(\Rightarrow\) 10	clear

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number	Statement
30:	Ordering Principle: Every set can be linearly ordered.
10:	\(C(\aleph_{0},< \aleph_{0})\):  Every denumerable family of non-empty finite sets has a choice function.

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