Preimage of Zero of Homomorphism is Submagma

Theorem
Let $\left({S, *}\right)$ be a magma.

Let $\left({T, \circ}\right)$ be a magma with a zero element $0$.

Let $\phi:S \to T$ be a magma homomorphism.

Then $\left({\phi^{-1} \left({0}\right), *}\right)$ is a submagma of $\left({S, *}\right)$.

Proof
Let $x, y \in \phi^{-1} \left({0}\right)$.

It is to be shown that:
 * $x * y \in \phi^{-1} \left({0}\right)$

Thus:

Hence the result.