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We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 429-p given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 429-p

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.
429-p:	(Where \(p\) is a prime) B: Every vector space over \(\mathbb Z_p\) has a basis.  (\(\mathbb Z_p\) is the \(p\) element field.) \ac{Bleicher} \cite{1964}, \ac{Rubin, H.\/Rubin, J \cite{1985, p.119, B}.

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