Composite of Group Homomorphisms is Homomorphism/Proof 1

Theorem

Let:

$\struct {G_1, \circ}$

$\struct {G_2, *}$

$\struct {G_3, \oplus}$

be groups.

Let:

$\phi: \struct {G_1, \circ} \to \struct {G_2, *}$

$\psi: \struct {G_2, *} \to \struct {G_3, \oplus}$

be homomorphisms.

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

Proof

A specific instance of Composite of Homomorphisms on Algebraic Structure is Homomorphism.

$\blacksquare$