Can a mirrorless camera produce images as good as DSLR?

Referring just to still, stationary images, can a nice mirrorless model, like some of the Sony nex's produce equally as good an image as a Nikon D7100 or D610?

Most of the issue is the quality of the lens not so much as the box it is attached to.

The sensor is on the same size scale as an SLR. The lenses can be good. So the answer is yes. The main difference is the absence of a mirror and having an electronic viewfinder. This makes it possible to make the package smaller and lighter. Some don't care for the electronic viewfinder. Others think it's great.

Yes!
Provided the lenses are equally good.