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

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

It must be shown that $x*y \in \phi^{-1}(0)$.

Hence the result.