Implications

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We have the following indirect implication of form equivalence classes:

381 \(\Rightarrow\) 418 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
381 \(\Rightarrow\) 418	Metric spaces and the axiom of choice, De-la-Cruz-Hall-Howard-Keremedis-Rubin-2002A[2002A], Math. Logic Quart.

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

Howard-Rubin Number	Statement
381:	DUM:  The disjoint union of metrizable spaces is metrizable.
418:	DUM(\(\aleph_0\)): The countable disjoint union of metrizable spaces is metrizable.

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