Axiom Of Choice

We have the following indirect implication of form equivalence classes:

395 \(\Rightarrow\) 395 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
395 \(\Rightarrow\) 395

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

Howard-Rubin Number	Statement
395:	\(MC(LO,LO)\): For each linearly ordered family of non-empty linearly orderable sets \(X\), there is a function \(f\) such that for all \(x\in X\) \(f(x)\) is a non-empty, finite subset of \(x\).
395:	\(MC(LO,LO)\): For each linearly ordered family of non-empty linearly orderable sets \(X\), there is a function \(f\) such that for all \(x\in X\) \(f(x)\) is a non-empty, finite subset of \(x\).

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