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We have the following indirect implication of form equivalence classes:

6 \(\Rightarrow\) 0 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
6 \(\Rightarrow\) 0

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

Howard-Rubin Number	Statement
6:	\(UT(\aleph_0,\aleph_0,\aleph_0,\Bbb R)\): The union of a denumerable  family  of denumerable subsets of \({\Bbb R}\) is denumerable.
0:	\(0 = 0\).

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