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We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 405 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 405

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

Howard-Rubin Number	Statement
1:	\(C(\infty,\infty)\):  The Axiom of Choice: Every  set  of  non-empty sets has a choice function.
405:	Every infinite set can be partitioned into sets each of which is countable and has at least two elements.

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