Isomorphism Preserves Semigroups

Theorem
Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be algebraic structures.

Let $\phi: \left({S, \circ}\right) \to \left({T, *}\right)$ be an isomorphism.

If $\left({S, \circ}\right)$ is a semigroup, then so is $\left({T, *}\right)$.