Implications

We have the following indirect implication of form equivalence classes:

21 \(\Rightarrow\) 0
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
21 \(\Rightarrow\) 0

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

Howard-Rubin Number Statement
21:

If \(S\) is well ordered, \(\{A_{x}: x\in S\}\) and \(\{B_{x}: x\in S\}\) are families of pairwise disjoint sets, and \(|A_{x}| = |B_{x}|\) for all \(x\in S\), then \(|\bigcup_{x\in S}A_{x}|= |\bigcup_{x\in S} B_{x}|\). G\.

0:  \(0 = 0\).

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