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We have the following indirect implication of form equivalence classes:

16 \(\Rightarrow\) 352 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
16 \(\Rightarrow\) 352	On first and second countable spaces and the axiom of choice, Gutierres, G 2004, Topology and its Applications.

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

Howard-Rubin Number	Statement
16:	\(C(\aleph_{0},\le 2^{\aleph_{0}})\):  Every denumerable collection of non-empty sets  each with power \(\le  2^{\aleph_{0}}\) has a choice function.
352:	A countable product of second countable spaces is second countable.

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