/sci/ - Science & Math

Could somebody point me to a formal proof of the concept that if we have a tree with [math]\ge 2[/math] vertices and the degree of the first vertex is [math]n[/math] and the degree of the second vertex is [math]m[/math], the tree has [math]\ge n + m - 2[/math] leaves? It's easy to see why it has to be true when looking at graphical representation like the picture related and using the conditions that a tree has to be a connected graph and cannot contain cycles. However, I feel like my current approach is too simplistic and would like to see a more thought out version. I tried Googling, but didn't really find anything relevant.