Saalschütz's theorem

Statement

Saalschütz's theorem (Saalschütz 1890) states

$${}_3F_2 (a,b, -n;c, 1+a+b-c-n;1)= \frac{(c-a)_n(c-b)_n}{(c)_n(c-a-b)_n}.$$

For extension of this theorem, see a research paper by Rakha & Rathie. According to Andrews, it was in fact first discovered by Pfaff in 1797.