 Hybrid logic can be translated into first-order logic with equality, and (a fragment of) first-order logic with equality can be translated back into (a fragment of) hybrid logic. The first-order language under consideration has a 1-place predicate symbol \(\mathtt{p^*}\) corresponding to each ordinary propositional symbol \(\mathtt{p}\) of modal logic, a 2-place predicate symbol \(\mathtt{R}\), and a 2-place predicate symbol \(\mathtt{=}\). Of course, the predicate symbol \(\mathtt{p^*}\) will be interpreted such that it relativises the interpretation of the corresponding modal propositional symbol \(\mathtt{p}\) to worlds, the predicate symbol \(\mathtt{R}\) will be interpreted using the accessibility relation, and the predicate symbol \(\mathtt{=}\) will be interpreted using the identity relation on worlds. We let \(\mathtt{a}, \mathtt{b}, \mathtt{c},\ldots\) range over first-order variables. The language does not have constant or function symbols. We shall identify first-order variables with nominals of hybrid logic.