P20: He who imagines that what he hates is destroyed will rejoice.

Dem.: The Mind (by P13) strives to imagine those things that exclude the existence of things by which the Body’s power of acting is diminished or restrained, i.e. (by P13 S), strives to imagine those things that exclude the existence of things it hates. So the image of a thing that excludes the existence of what the Mind hates aids this striving of the Mind, i.e. (by P11 S), affects the Mind with Joy. Therefore, he who imagines that what he hates is destroyed will rejoice, q.e.d.