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We have the following indirect implication of form equivalence classes:

89 \(\Rightarrow\) 118 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
90 \(\Rightarrow\) 118	Horrors of topology without AC: A non-normal orderable space, van Douwen, E.K. 1985, Proc. Amer. Math. Soc.

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.
118:	Every linearly orderable topological space is normal.  Birkhoff [1967], p 241.

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