Substructure of Entropic Structure is Entropic

Theorem
Let $\struct {S, \odot}$ be an entropic structure:
 * $\forall a, b, c, d \in S: \paren {a \odot b} \odot \paren {c \odot d} = \paren {a \odot c} \odot \paren {b \odot d}$

Let $\struct {T, \odot_T}$ be a substructure of $\struct {S, \odot}$.

Then $\struct {T, \odot_T}$ is also an entropic structure.