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We have the following indirect implication of form equivalence classes:

343 \(\Rightarrow\) 154 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
343 \(\Rightarrow\) 154	Products of compact spaces and the axiom of choice II , Hall, E. 2002, Math. Logic Quart.

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

Howard-Rubin Number	Statement
343:	A product of non-empty, compact \(T_2\) topological spaces is non-empty.
154:	Tychonoff's Compactness Theorem for Countably Many \(T_2\) Spaces: The product of countably many \(T_2\) compact spaces is compact.

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