 The premises guarantee that all \(\phi_2\)-worlds in \(R(w)\) are \(\phi_1\)-worlds, and that all \(\phi_1\)-worlds in \(R(w)\) are  \(\psi\)-worlds. That gives one the relationships depicted  in Figure 8. To show that  \(\phi_2\strictif\psi\) follows, suppose that w is a  \(\phi_2\)-world in \(R(w)\). As  Figure 8  makes evident, w must then be a \(\psi\)-world.