Axiom Of Choice

We have the following indirect implication of form equivalence classes:

344 \(\Rightarrow\) 344 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
344 \(\Rightarrow\) 344

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

Howard-Rubin Number	Statement
344:	If \((E_i)_{i\in I}\) is a family of non-empty sets, then there is a family \((U_i)_{i\in I}\) such that \(\forall i\in I\), \(U_i\) is an ultrafilter on \(E_i\).
344:	If \((E_i)_{i\in I}\) is a family of non-empty sets, then there is a family \((U_i)_{i\in I}\) such that \(\forall i\in I\), \(U_i\) is an ultrafilter on \(E_i\).

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