Open Projection and Closed Graph Implies Quotient is Hausdorff

Theorem
Let $\RR \subseteq X \times X$ be an equivalence relation on a topological space $X$.

Let $X / \RR$ be the quotient space.

Let $p$ denote the quotient mapping.

Let:
 * $\RR$ be closed in $X \times X$
 * $p$ be open

Then $X / \RR$ is Hausdorff.

Also see

 * Hausdorff Space iff Diagonal Set on Product is Closed