Many popular ontology languages are based on (subsets of) first-order predicate logic, where classes are modeled as unary predicates and properties as binary predicates. Specifically, the ontology language OWL DL is based on the Description Logic SHOIQ. F-Logic is an ontology language which is also based on first-order logic, but classes and properties are modeled as terms, rather than predicates. In this paper we define a translation from predicate-based ontologies to F-Logic ontologies and show that this translation preserves entailments for large classes of ontologies, including most of OWL DL. We define the class of equality-safe (E-safe) formulas, show that the Description Logic SHIQ is E-safe, and show that the translation preserves validity of E-safe formulas. Finally, we use these results to close the open problems of layering F-Logic programming on top of Description Logic Programs and language layering in WSML.