Bredt's Rule - Explained with Proof | Applications | Problems | IITian Explains 

In its original form, Bredt's Rule stated that bridged ring systems and pinane cannot have a double bond at the bridgehead position .
In principle, the Bredt’s rule is simply a consequence of the strain induced by a planar bridgehead carbon.
A few key concepts to keep in mind when understanding the Bredt’s rule are -
A double bond comprises one sigma bond and a one π bond.
The pi bond is formed by the overlap of p-orbitals. Therefore these p-orbitals must be on the same planar. If they are not, the chances of an overlap are negligible and the bond formed will be unstable.
A double bond on a bridgehead would be equivalent to having a trans pi double bond on a ring, which is not stable for small rings (fewer than eight atoms) due to a combination of ring strain, and angle strain (nonplanar alkene).
Bridged bicyclic compounds can only exhibit a double bond at a bridgehead position if one of the rings has at least eight carbon atoms
And therefore, bridgehead double bonds are unstable due to poor orbital overlap.
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IITian Explains