Class

Subclass

Let 𝐴,𝐵 be classes. A subclass 𝐴 ⊆𝐵 is a class whose elements are all elements of 𝐵, set i.e.

𝐴⊆𝐵def⟺(∀𝑥)[𝑥∈𝐴⟹𝑥∈𝐵]

A proper subclass is is a subset that is not equal to its superset, i.e.

𝐴⊊𝐵def⟺[𝐴⊆𝐵∧𝐴≠𝐵]

noting the Axiom of Extensionality for Classes. Note these definitions are identical to that of a subset, but with set replaced by class.

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