Player being hit twice?

In my network arena shooter, If a player shoots a gun, it spawns a projectile on the server - but also on each of the clients connected (or else they wouldn’t see said projectile - correct?).

The problem now is that any connected client, get hit by the projectile on the server AND the projectile on the client - BOTH causing that player damage.

What is an elegant why around this ?

The player hp should NEVER EVER be handled by client, thats just asking for a cheater to /kill everyone, have the shot visually happen on all clients and server, but the hp change and actual bullet should happen on the server, replicating the change to all the clients.