The Sony a77 isn't technically a DSLR. Unlike a single lens reflex camera, in which the mirror flips up out of the way to clear the light path to the shutter and sensor or film, the mirror in the a77 is a pellicle style mirror and fixed in place.
The pellicle mirror lets most of the light pass through to the sensor while reflecting some of it upward. Where the prism or mirror box would be on a normal SLR was a phase detection autofocus sensor. The viewfinder was electronic, like on a mirrorless camera. Mirrorless cameras of the time could only use contrast detection autofocus, which was much slower and more prone to focus hunting.
Sony called these Single-Lens Translucent, or "SLT" cameras. Further developments in sensor tech rendered this obsolete in fairly short order. The SLT era at Sony was brief, with the first being launched in 2010 and the final model appearing in 2016.

