 Note that the calculus just described is quantifier-free. Quantifiers  can be defined as follows: \[ \begin{align} \exists x A(x) &amp;\equiv A(\varepsilon x A) \\ \forall x A(x) &amp;\equiv A(\varepsilon x (\neg A)) \end{align} \] The usual quantifier axioms   and rules can be derived from these, so the definitions above serve to embed first-order logic in the epsilon calculus. The converse is, however, not true: not every formula in the epsilon calculus is the image of an ordinary quantified formula under this embedding. Hence, the epsilon calculus is more expressive than the predicate calculus, simply because epsilon terms can be combined in more complex ways than quantifiers.