We have the following indirect implication of form equivalence classes:

113 \(\Rightarrow\) 113
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
113 \(\Rightarrow\) 113 Products of compact spaces in the least permutation model, Brunner, N. 1985a, Z. Math. Logik Grundlagen Math.

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

Howard-Rubin Number Statement
113:

Tychonoff's Compactness Theorem for Countably Many Spaces: The product of a countable set of compact spaces is compact.

113:

Tychonoff's Compactness Theorem for Countably Many Spaces: The product of a countable set of compact spaces is compact.

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