Beth property

A logic is said to have the Beth property if whenever a predicate $R$ is implicitly definable by $\varphi$ (i.e. if all models have at most one unique extension satisfying $\varphi$), then $R$ is explicitly definable relative to $\varphi$ (i.e. there is a $\psi$ not containing $R$,such that $\varphi \vDash \forall x_1,..,x_n(R(x_1,\mathrm{\dots },x_n)\leftrightarrow \psi (x_1,\mathrm{\dots },x_n))$).