Null Ring is Subring of Ring

Theorem
Let $R$ be a ring.

Then the null ring is a subring of $R$.

Proof
From Null Ring is Ring, the null ring $\struct {\set {0_R}, +, \circ}$ is a ring.

We also have that $\set {0_R}$ is a subset of $R$

Hence the result by definition of subring.