Snapshots are not linked with the instances or the images from which they were created. They are just another independent image. You can delete the original instance or the image.

You can delete the image from which an instance was launched without affecting the instance. This includes images that were created by snapshotting an instance.

Taking a snapshot just saves the state of the original image and is no longer linked to it. It isn't a reference to the original image, it is just a new image. Therefore deleting the underlying image will not affect the snapshot.