Congruence of Sum with Constant

Theorem
Let $a, b, z \in \R$.

Let $a$ be congruent to $b$ modulo $z$, i.e. $a \equiv b \ \left({\bmod\, z}\right)$.

Then:
 * $\forall c \in \R: a + c \equiv b + c \ \left({\bmod\, z}\right)$.

Proof
Follows directly from the definition of Modulo Addition: