We have the following indirect implication of form equivalence classes:

13 \(\Rightarrow\) 13
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
13 \(\Rightarrow\) 13 Zermelo's Axiom of Choice, Moore, [1982]

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

Howard-Rubin Number Statement
13:

Every Dedekind finite subset of \({\Bbb R}\) is finite.

13:

Every Dedekind finite subset of \({\Bbb R}\) is finite.

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