Axiom Of Choice

We have the following indirect implication of form equivalence classes:

392 \(\Rightarrow\) 337 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
392 \(\Rightarrow\) 394	clear
394 \(\Rightarrow\) 337	clear

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

Howard-Rubin Number	Statement
392:	\(C(LO,LO)\): Every linearly ordered set of linearly orderable sets has a choice function.
394:	\(C(WO,LO)\): Every well ordered set of non-empty linearly orderable sets has a choice function.
337:	\(C(WO\), uniformly linearly ordered): If \(X\) is a well ordered collection of non-empty sets and there is a function \(f\) defined on \(X\) such that for every \(x\in X\), \(f(x)\) is a linear ordering of \(x\), then there is a choice function for \(X\).

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