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We have the following indirect implication of form equivalence classes:

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

Implication	Reference
259 \(\Rightarrow\) 0

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

Howard-Rubin Number	Statement
259:	\(Z(TR\&C,W)\): If \((X,R)\) is a transitive and connected relation in which every well ordered subset has an upper bound, then \((X,R)\) has a maximal element.
0:	\(0 = 0\).

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