I have been trying to check that two things are equal for a while now, Mathematica appears to say that they are but I can't for the life of me figure out how to show it (without just saying 'computer says yes'), does anybody know a 'nice' way to show the following expression is true?

$$\binom{v + w + d - 1}{d} = \sum_{a=0}^d \binom{v+a-1}{a} \binom{w + d - a - 1}{d-a}$$