Steel jacketed 7.62 x 54r ammo?

So i got some ammo for my mosin nagant at a local gun shop. Don't ask why but i took one of the rounds apart. In doing so i found the bullet (that is the projectile that leaves the front of the gun) has a lead core with a steel jacket. One part of me says "the mosin is a tough gun thats been used for over 100 years, it'll be fine.". However another part of me says "I took months to climb through 400 dirty, shitty mosins to find the best one, with GOOD rifling. So i cant shoot something that has a steel jacket. It will grind down all the groves. ". Witch is right? Will the gun be fine, or will the steel stuff shorten the guns lifespan?