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We have the following indirect implication of form equivalence classes:

45-n \(\Rightarrow\) 33-n given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
45-n \(\Rightarrow\) 33-n	clear

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

Howard-Rubin Number	Statement
45-n:	If \(n\in\omega-\{0,1\}\), \(C(\infty,n)\): Every set of \(n\)-element sets has a choice function.
33-n:	If \(n\in\omega-\{0,1\}\), \(C(LO,n)\):  Every linearly ordered set of \(n\) element sets has  a choice function.

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