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We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 425 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 425

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.
425:	For every first countable topological space \((X, \Cal T)\) there is a family \((\Cal D(x))_{x \in X}\) such that \(\forall x \in X\), \(D(x)\) countable local base at \(x\).  \ac{Gutierres} \cite{2004} and note 159.

Comment: