The following argument is valid, and is sound if we take the conditional in (2) to be material.
- (Premise) In despairing, one engages in a vice.
- (Premise) If there is no afterlife, it is sometimes appropriate to despair.
- (Premise) It is never appropriate to engage in a vice.
- So, there is an afterlife.
Let me say a little about (2). Despair is appropriate in situations of objective hopelessness. But if there is no afterlife, then when one has misspent one's life in wickedness, and is now facing death with no opportunity to make things up to those whom one has mistreated, then despair is appropriate.
If there is an afterlife, then one can hope for mercy or justice.