Restriction of Associative Operation is Associative

Theorem
Let $$\left({S, \circ}\right)$$ be an algebraic structure.

Let $$T \subseteq S$$.

If the operation $$\circ$$ is associative on $$\left({S, \circ}\right)$$, then it is also associative on a restriction $$\left({T, \circ \restriction_T}\right)$$.

Proof
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