 Among these deeper axioms was Frege’s ill-fated Basic Law V. This, like HP, is a double-abstraction principle. Basic Law V, however, allows for the abstraction of classes, and the equivalence relation by which this is effected is the relation of coextensiveness among defining predicates. Frege never raised the Julius Caesar objection against his Basic Law V. Using modern notation, Basic Law V can be stated as the following axiom schema, in which Φ and Ψ are placeholders for formulas: 