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We have the following indirect implication of form equivalence classes:

66 \(\Rightarrow\) 428 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
66 \(\Rightarrow\) 428	clear

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

Howard-Rubin Number	Statement
66:	Every vector space over a field has a basis.
428:	\(\exists F\) B\((F)\):  There is a field \(F\) such that every vector space over \(F\) has a basis. \ac{Bleicher} \cite{1964}, \ac{Rubin, H.\/Rubin, J \cite{1985, p.119, B}.

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