Axiom Of Choice

We have the following indirect implication of form equivalence classes:

1 \(\Rightarrow\) 402 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
1 \(\Rightarrow\) 402

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.
402:	\(KW(WO,LO)\), The Kinna-Wagner Selection Principle for a well ordered set of linearly orderable sets: For every well ordered set of linearly orderable sets \(M\) there is a function \(f\) such that for all \(A\in M\), if \(\|A\|>1\) then \(\emptyset\neq f(A)\subsetneq A\).

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