 Prime-row binomial coefficient divisibility

For a prime number $p$, the identity $r!\left(\genfrac{}{}{0ex}{}{p}{r}\right)=p(p-1)\cdots (p-r+1)$ has right side divisible by $p$, while $r!$ is coprime to $p$. Cancellation in modular arithmetic proves the divisibility.

// Target: combinatorics.bigb