We have the following indirect implication of form equivalence classes:

203 \(\Rightarrow\) 194
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
203 \(\Rightarrow\) 94 note-67
94 \(\Rightarrow\) 194 clear

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

Howard-Rubin Number Statement
203:

\(C\)(disjoint,\(\subseteq\Bbb R)\): Every partition of \({\cal P}(\omega)\) into non-empty subsets has a choice function.

94:

\(C(\aleph_{0},\infty,{\Bbb R})\): Every denumerable family of non-empty sets of reals  has a choice function. Jech [1973b], p 148 prob 10.1.

194:

\(C(\varPi^1_2)\) or \(AC(\varPi^1_2)\): If \(P\in \omega\times{}^{\omega}\omega\), \(P\) has domain \(\omega\), and \(P\) is in \(\varPi^1_2\), then there is a sequence of elements \(\langle x_{k}: k\in\omega\rangle\) of \({}^{\omega}\omega\) with \(\langle k,x_{k}\rangle \in P\) for all \(k\in\omega\). Kanovei [1979].

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