Null Module Submodule of All

Theorem
Let $\struct {G, +_G, \circ}_R$ be an $R$-module.

Then the null module:
 * $\struct {\set {e_G}, +_G, \circ}_R$

is a submodule of $\struct {G, +_G, \circ}_R$.

Proof
From Trivial Subgroup is Subgroup, the trivial subgroup is a subgroup of the group $\struct {G, +_G}$.

The result follows from the Submodule Test.