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We have the following indirect implication of form equivalence classes:

181 \(\Rightarrow\) 353 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
181 \(\Rightarrow\) 8	clear
8 \(\Rightarrow\) 353	Disasters in metric topology without choice, Keremedis, K. 2002, Comment. Math. Univ. Carolinae

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

Howard-Rubin Number	Statement
181:	\(C(2^{\aleph_0},\infty)\): Every set \(X\) of non-empty sets such that \(|X|=2^{\aleph_0}\) has a choice function.
8:	\(C(\aleph_{0},\infty)\):
353:	A countable product of first countable spaces is first countable.

Comment: