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We have the following indirect implication of form equivalence classes:

14 \(\Rightarrow\) 410 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
14 \(\Rightarrow\) 410	note-23

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

Howard-Rubin Number	Statement
14:	BPI: Every Boolean algebra has a prime ideal.
410:	RC (Reflexive Compactness): The closed unit ball of a reflexive normed space is compact for the weak topology.

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