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We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 348 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 348

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.
348:	If \(G\) is a group and \(X\) and \(Y\) both freely generate \(G\) then \(|X| = |Y|\).

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