Integer is Congruent Modulo Divisor to Remainder/Corollary

Corollary to Integer is Congruent Modulo Divisor to Remainder
Let $a \equiv b \pmod m$ denote that $a$ and $b$ are congruent modulo $m$.

$a \equiv b \pmod m$ $a$ and $b$ have the same remainder when divided by $m$.

Proof
Follows directly from:
 * Integer is Congruent Modulo Divisor to Remainder
 * Congruence Modulo Real Number is Equivalence Relation.