Walls and Ceilings - Is it safe to remove one cross bridge bewteen ceiling joists?

Hi, I am installing recessed lights in my living room. The ceiling is finished and it is between the first and the second floor. Everything was going well untill I got to the last hole - when I drilled it in the ceiling I discovered that there is a cross bridge between the joists in that exact spot. Unfortunately Ican't move the light anywhere else besides that spot. I am kinda upset since I considered all the joists and other boards very carefuly but had no way of knowing that I may hit a cross bridge. I don't have any construction experience but from doing some light reading I understand that cross bridging adds some structural integrity and helps illiminate squeaks and such by basically preventing joists from moving sideways. My question is: Is it safe to remove one cross bridge in that particular spot? My guess is that it should be ok to do that since there are other cross bridges between other studs and in addition I could try installing a metal cross bridge a few inches to the side from where this one is now if it is necessary. Anyone with construction knowledge or experience could give me an advice please? I am afraid to remove it if it will cause some structural integrity issue. Please help.

Thanks!

If you have a drywall ceiling then I would say take it out. Relocating would be the best but if you remove it won't be a big deal.

coops is correct if you have a drywall ceiling then that should act as the rigid horizontal member which in a sense takes the place of the bridging.

You really shouldn't have any problems. If it makes you feel better you can relocate it but it really isn't required.

Thanks to both of you for your replies! Definitely made me feel more confident about removing this bridging. All the holes are all set now and ready for lights! Will be running wires today.

Again, thanks for help!