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We have the following indirect implication of form equivalence classes:

63 \(\Rightarrow\) 70 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
63 \(\Rightarrow\) 70	clear

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

Howard-Rubin Number	Statement
63:	\(SPI\): Weak ultrafilter principle: Every infinite set has a non-trivial ultrafilter. Jech [1973b], p 172 prob 8.5.
70:	There is a non-trivial ultrafilter on \(\omega\). Jech [1973b], prob 5.24.

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