Equality is Equivalence Relation

Theorem
Equals is an equivalence relation.

Proof
This follows from the axioms of equality:


 * Equality is Reflexive: $\forall a: a = a$.
 * Equality is Symmetric: $\forall a, b: a = b \implies b = a$.
 * Equality is Transitive: $\forall a, b, c: a = b \land b = c \implies a = c$.

The result follows from the definition of an equivalence relation.