Implications

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We have the following indirect implication of form equivalence classes:

51 \(\Rightarrow\) 51 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
51 \(\Rightarrow\) 51	L’axiome de M. Zermelo et son rˆole dans la th´eorie des ensembles et l’analyse, Sierpi'nski, W. 1918, Bull. Int. Acad. Sci. Cracovie Cl. Math. Nat.

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

Howard-Rubin Number	Statement
51:	Cofinality Principle: Every linear ordering has a cofinal sub well ordering.  Sierpi\'nski [1918], p 117.
51:	Cofinality Principle: Every linear ordering has a cofinal sub well ordering.  Sierpi\'nski [1918], p 117.

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