Restriction of Associative Operation is Associative

Theorem
Let $\struct {S, \circ}$ be an algebraic structure.

Let $T \subseteq S$.

Let $\circ_T$ denote the restriction of $\circ$ to $T$.

Let the operation $\circ$ be associative on $\struct {S, \circ}$.

Then $\circ_T$ is associative on $\struct {T, \circ_T}$.