Bredt's rule is a consequence of the fact that having a double bond on a bridgehead or carbocation is not stable for small rings (fewer than eight atoms) due to a combination of ring strain and angle strain (nonplanar alkene). Since SN1 reaction involves a carbocation intermediate, and such intermediate is not possible here, the SN1 mechanism is ruled out.
SN2 reaction involves a backside attack from the leaving group. Due to stearic hindrance to the backside attack, such reaction is also not possible. In general, nucleophilic substitution is not possible.
