Showing a relation between binomial and negative binomial analytically

Question

If $X$ is binomial random variable $B(n,p)$ and Y is negative binomial $(r,p)$, How can I show that $F_X(r-1) = 1- F_Y(n-r)$.

While it is possible to show that using the definition of binomial and negative binomial, I am more interested in showing that directly using their p.m.fs.