| context | $X$ |
| definiendum | $ \sim \in \text{EquivRel}(X) $ |
| context | $ \sim \in \mathrm{Rel}(X) $ |
| $x,y,z\in X$ |
| postulate | $ x\sim x $ |
| postulate | $ x\sim y \Leftrightarrow y\sim x $ |
| postulate | $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ |
The relation $\sim$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence
Wikipedia: Equivalence relation