Implications

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We have the following indirect implication of form equivalence classes:

58 $\Rightarrow$ 0 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
58 $\Rightarrow$ 0

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

Howard-Rubin Number	Statement
58:	There is an ordinal $\alpha$ such that $\aleph(2^{\aleph_{\alpha }})\neq\aleph_{\alpha +1}$. ($\aleph(2^{\aleph_{\alpha}})$ is Hartogs' aleph, the least $\aleph$ not $\le 2^{\aleph _{\alpha}}$.) Mathias [1979], p 126.
0:	$0 = 0$.

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