Thinking...
This is a simple logic question about categorical syllogisms. If all A are
B (A ⊆ B) and all B are C (B ⊆ C), then by transitivity of subset relation,
relation, all A must be C (A ⊆ C). This is the classic Barbara syllogism in
in Aristotelian logic.
The answer is definitively Yes. I should explain concisely in one sentence
as requested.
...done thinking.
**Yes.** By transitivity: if every A is a B and every B is a C, then every
A is necessarily a C (A ⊆ B ⊆ C ⇒ A ⊆ C).