Axiom Of Choice

We have the following indirect implication of form equivalence classes:

143 \(\Rightarrow\) 143 given by the following sequence of implications, with a reference to its direct proof:

Implication	Reference
143 \(\Rightarrow\) 143

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

Howard-Rubin Number	Statement
143:	\(H(C,TR)\): If \((X,R)\) is a connected relation (\(u\neq v\rightarrow u\mathrel R v\) or \(v\mathrel R u\)) then \(X\) contains a \(\subseteq\)-maximal transitive subset.
143:	\(H(C,TR)\): If \((X,R)\) is a connected relation (\(u\neq v\rightarrow u\mathrel R v\) or \(v\mathrel R u\)) then \(X\) contains a \(\subseteq\)-maximal transitive subset.

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