Congruence Relation on Naturals for Addition Distinct from Equality is Dipper Relation

Theorem
Let $\RR$ be a congruence relation for addition on the natural numbers $\N$.

Let $\RR$ be distinct from the equality relation on $\N$.

Then there exist $m \in \N$ and $n \in \N_{>0}$ such that:
 * $\RR = \RR_{m, n}$

where $\RR_{m, n}$ denotes the dipper relation.