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We have the following indirect implication of form equivalence classes:

66 \(\Rightarrow\) 111 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
66 \(\Rightarrow\) 110	clear
110 \(\Rightarrow\) 111	Disasters in metric topology without choice, Keremedis, K. 2002, Comment. Math. Univ. Carolinae

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

Howard-Rubin Number	Statement
66:	Every vector space over a field has a basis.
110:	Every vector space over \(\Bbb Q\) has a basis.
111:	\(UT(WO,2,WO)\): The union of an infinite well ordered set of 2-element sets is an infinite well ordered set.

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