Natural Numbers form Subsemiring of Integers

Theorem
The semiring $$\left({\N, +, \times}\right)$$ of natural numbers forms a subsemiring of the ring of integers $$\left({\Z, +, \times}\right)$$.

Proof
We have that Natural Numbers form Commutative Semiring.

From Natural Numbers are Non-Negative Integers we have that $$\N$$ is a subset of $$\Z$$.

Hence the result, from the definition of subsemiring.