Implications

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We have the following indirect implication of form equivalence classes:

3 \(\Rightarrow\) 186 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
3 \(\Rightarrow\) 186	Set theory for the mathematician, Rubin, [1967]

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

Howard-Rubin Number	Statement
3:	\(2m = m\): For all infinite cardinals \(m\), \(2m = m\).
186:	Every pair of cardinal numbers has a least upper bound (in the usual cardinal ordering.)

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