homomorphic image of a $\mathrm{\Sigma }$-structure is a $\mathrm{\Sigma }$-structure

Let $\mathrm{\Sigma }$ be a fixed signature, and $𝔄$ and $𝔅$ two structures for $\mathrm{\Sigma }$. If $f:𝔄\to 𝔅$ is a homomorphism, then $\mathrm{im}(f)$ is a structure for $\mathrm{\Sigma }$.