SLR (single lens reflex) has a mirror, with either a pentaprism or pentamirror (where you stick your eyeball) to show you the view as it is through the lens.
SLR = Single Lens Reflex
Technically, this does not signify the requirement of a mirror or not. It just specifies that the picture is exposed using the same lens that is used for framing.
Not so sure about that... depends on how you define the meaning of 'reflex'. The 'reflex' can refer either to the use of a mirror (as in reflection and is the meaning for a TLR) or the automatic removal of the mirror (as in reflex action) when taking the shot. Probably both for SLR and DSLR. Take the mirror out of the equation and you just a SL without the R.
What hath Bob wrought?