  Quantification is possibilist—domains are constant. But, as was discussed in Section 3.2.1, varying domains can be brought in indirectly by using the existence predicate, \(E\), and this allows us to introduce actualist quantification definitionally. Let \(\forall^{E}xX\) abbreviate \(\forall x(E(x) \supset X)\), and let \(\exists^{E}xX\) abbreviate \(\exists x(E(x)  \wedge X)\). Then, while  \(\forall x\phi (x) \supset \phi (y)\) is valid, assuming \(y\) is free for \(x\) in \(\phi (x)\), we do not have the validity of \(\forall^{E}x\phi (x) \supset \phi (y)\). What we have instead is the validity of \([\forall^{E}x\phi (x)  \wedge E(y)] \supset \phi (y)\).