A subclass of B

A instance of 'type of B'

B subclass of 'C'

B instance of 'type of C'

C subclass of 'D'

C instance of 'type of D'

It's a bit more subtle than that, as, let's take the Taxonomy example, and take the <animal> class.

Old classifications used to take <fish> as a taxon. It is proved right now that fish is not a clade. It's still a subclass of <animal> though.

I claim <fish> subclass of <animal> is still correct.

<fish> is an old taxon. But <fish> instance of <clade> is not true.

If someone want to search for direct subclasses of "animal", he would still have "fish" as a result, maybe. Although if he is interested in clades only my approach works, and he would get a closer approximation of what modern taxonomy tree is.