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We have the following indirect implication of form equivalence classes:

413 \(\Rightarrow\) 0 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
413 \(\Rightarrow\) 0

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

Howard-Rubin Number	Statement
413:	Every infinite set \(S\) is the union of a set, well-ordered by inclusion, of subsets which are non-equipollent to \(S\).
0:	\(0 = 0\).

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