combinatorics - Combinatorial identity: summation of stars and bars

I noticed that the following identity for a summation of stars and bars held for specific $k$ but I was wondering if someone could provide a general proof via combinatorics or algebraic manipulation. I wouldn't be surprised if this is a known result; it looks very similar to the Hockey Stick identity.

$$\sum_{i=0}^k {d+i-1 \choose d-1} = {d+k \choose k}$$

The left can be immediately rewritten as $\sum_{i=0}^k {d+i-1 \choose i}$ if it helps inspire intuition.