We have the following indirect implication of form equivalence classes:

110 \(\Rightarrow\) 110
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
110 \(\Rightarrow\) 110 Existence of a basis implies the axiom of choice, Blass, A. 1984a, Contemporary Mathematics

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

Howard-Rubin Number Statement
110:

Every vector space over \(\Bbb Q\) has a basis.

110:

Every vector space over \(\Bbb Q\) has a basis.

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