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We have the following indirect implication of form equivalence classes:

352 \(\Rightarrow\) 31 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
352 \(\Rightarrow\) 31	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
352:	A countable product of second countable spaces is second countable.
31:	\(UT(\aleph_{0},\aleph_{0},\aleph_{0})\): The countable union theorem:  The union of a denumerable set of denumerable sets is denumerable.

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