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We have the following indirect implication of form equivalence classes:

60 \(\Rightarrow\) 421 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
60 \(\Rightarrow\) 231	Cardinals and the Boolean prime ideal theorem, Tsukada, N. 1977, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A
231 \(\Rightarrow\) 421	clear

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

Howard-Rubin Number	Statement
60:	\(C(\infty,WO)\): Every set of non-empty, well orderable sets has a choice function. Moore, G. [1982], p 125.
231:	\(UT(WO,WO,WO)\): The union of a well ordered collection of well orderable sets is well orderable.
421:	\(UT(\aleph_0,WO,WO)\): The union of a denumerable set of well orderable sets can be well ordered.

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