What is the proper procedure to remove photos?

Someone will probably be able to help if you include more info. For instance :
iOS version? OS X version?
Currently syncing using -- iTunes (wired or wireless?)? iCloud Photo Library? Something else?

 

Delete the ones on your Mac. At the next sync, this will be replicated on your iPhone.

Can you delete photos on an iPhone that aren't in the Camera Roll? If you can, and they are still on your Mac, then they'll just get added again at the next sync.

 

If you delete them on your phone it will replicate the delete to your Mac (there is a deleted folder to recover anything accidentally deleted).

If you delete them on your Mac it will replicate the delete to your phone.

Apple has this thing where if you try to overthink it, you'll probably do more harm than good, it's not their fault though, Microsoft trained us.

If you delete anything on one Apple device that uses iCloud, it will remove it from all of your other iCloud devices.

 

Things have obviously changed since iOS6 then?

 

If you are using iCloud Photos, yes. There isn't enough information in the OPs statement to make a conclusive answer.

Things that should be included:
iOS Version
OSX Version (since he said photos I am assuming it is 10.10+)
Size of photo library (to the nearest .5 GB)
iCloud Drive storage size (free or paid plan at what tier)

As you had posted, the user will need to delete the photo from both their Mac and their Phone for the photo to be completely deleted if they are not using iCloud to store their photos.

As I assumed with 4000 photos they'd probably go for the iCloud Photos solution where they get backups, redundancy, the ability to have all of their photos on their phone without the need for much space, plus automated syncing of changes. It's honestly the best solution for large libraries, if the OP had < 500 photos then I'd say the old iTunes sync would be the better way to go. Cost to benefit.

 

Thanks for that. I'm not using iCloud.