 Thus universally quantified class variables are defined in terms of quantifiers ranging over predicative functions. Likewise for existential quantification:   \[ \tag*{∗20·071}   (\exists \alpha) \sdot f \alpha \ldot {=} \ldot  (\exists \phi) \sdot  f \{ \hat{z}(\phi\bang z)\} \quad\Df \]   or, in modern notation,  \[ \exists \alpha\, f\alpha =_\mathit{df} \exists \phi f\{z\mid\phi z\} \]   where \(\phi\) is a predicative function. 