Composite of Homomorphisms is Homomorphism/R-Algebraic Structure

Theorem
Let:
 * $\struct {S_1, *_1}_R$
 * $\struct {S_2, *_2}_R$
 * $\struct {S_3, *_3}_R$

be $R$-algebraic structures with the same number of operations.

Let:
 * $\phi: \struct {S_1, *_1}_R \to \struct {S_2, *_2}_R$
 * $\psi: \struct {S_2, *_2}_R \to \struct {S_3, *_3}_R$

be homomorphisms.

Then the composite of $\phi$ and $\psi$ is also a homomorphism.