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We have the following indirect implication of form equivalence classes:

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

Implication	Reference
405 \(\Rightarrow\) 0

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

Howard-Rubin Number	Statement
405:	Every infinite set can be partitioned into sets each of which is countable and has at least two elements.
0:	\(0 = 0\).

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