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We have the following indirect implication of form equivalence classes:

41 \(\Rightarrow\) 41 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
41 \(\Rightarrow\) 41	Zermelo's Axiom of Choice, Moore, 1982, page 326

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

Howard-Rubin Number	Statement
41:	\(W_{\aleph _{1}}\): For every cardinal \(m\), \(m \le \aleph_{1}\) or \(\aleph_{1}\le m \).
41:	\(W_{\aleph _{1}}\): For every cardinal \(m\), \(m \le \aleph_{1}\) or \(\aleph_{1}\le m \).

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