Deleting pictures on iphone and icloud

Basically yes. If your iPhone syncs with iCloud, then a photo you delete on your iPhone will also be deleted in iCloud.

You can check if your Photos is syncing with iCloud here:

Settings > Apple Account (Your Name) > iCloud > tap Photos and check if it is enabled.

If you are using iCloud photo library, that is correct.

iCloud photo library will sync your library to iCloud and all of your devices. Any changes made on one device will be reflected everywhere.