Let $X$ be a D11: Set such that
| (i) | \begin{equation} X \neq \emptyset \end{equation} |
| (ii) | ${\sim} \subseteq X \times X$ is an D178: Equivalence relation on $X$ |
| (iii) | $X / {\sim}$ is a D180: Quotient set of $X$ modulo ${\sim}$ |
Then
| (1) | $X / {\sim}$ is a D83: Proper set partition of $X$ |
| (2) | If $\mathcal{S}$ is a D83: Proper set partition of $X$, then there exists a D178: Equivalence relation ${\equiv} \subseteq X \times X$ on $X$ such that $\mathcal{S} = X / {\equiv}$ |