*can't* have common instances -- then you need to use
&gt; implication rather than bi-implication, since, obviously, from the fact
&gt; that C and C' happen to have no instances in common it doesn't follow that
&gt; they couldn't possibly have instances in common.
&gt; 
&gt; Note that this issue arises for most common properties of, and relations
&gt; among, classes; e.g., transitivity, reflexivity, subclass, etc.

Yes, and it also arises for any definition of any kind.

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