Congruence of Sum with Constant

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

Let $a$ be congruent to $b$ modulo $z$:
 * $a \equiv b \pmod z$

Then:
 * $\forall c \in \R: a + c \equiv b + c \pmod z$

Proof
Follows directly from the definition of Modulo Addition: