It’s a very tricky situation because “is life worth living” is a normative belief and thus subjective. That means you can’t objectively prove it to be logically true. On the other hand, once you make it clear that the “is life worth living” is a question about your personal self and not about features of objective reality, it might be easier for people to see that they need help.

Alternatively, distracting depressed people is probably the best bet.