In classical logic, the binary connective $\equiv$ such that

$\phi \equiv \psi \text{is}\{\begin{array}{l}\text{true}\text{if}\phi \text{and}\psi \text{are both true or both false}\\ \text{false}\text{otherwise}\end{array}$

Material equivalence of $\phi$ and $\psi$ is definable as the conjunction of $\phi \supset \psi$ and $\psi \supset \phi$, where $\supset$ is the material conditional.