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We have the following indirect implication of form equivalence classes:

89 \(\Rightarrow\) 90 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
89 \(\Rightarrow\) 90	The Axiom of Choice, Jech, 1973b, page 133

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

Howard-Rubin Number	Statement
89:	Antichain Principle:  Every partially ordered set has a maximal antichain. Jech [1973b], p 133.
90:	\(LW\):  Every linearly ordered set can be well ordered. Jech [1973b], p 133.

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