Congruence by Divisor of Modulus/Integer Modulus

Theorem
Let $r, s \in \Z$ be integers.

Let $a, b \in \Z$ such that $a$ is congruent modulo $r s$ to $b$, that is:
 * $a \equiv b \pmod {r s}$

Then:
 * $a \equiv b \pmod r$

and:
 * $a \equiv b \pmod s$