We have the following indirect implication of form equivalence classes:

40 \(\Rightarrow\) 165
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
40 \(\Rightarrow\) 165 clear

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

Howard-Rubin Number Statement
40:

\(C(WO,\infty)\):  Every well orderable set of non-empty sets has a choice function. Moore, G. [1982], p 325.

165:

\(C(WO,WO)\):  Every well ordered family of non-empty, well orderable sets has a choice function.

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