Let $T$ be a tree in which the largest degree of a node equals to $t$. Let $n\_1$ denote the number of nodes of degree $1$ in $G$. Prove that $n\_1 ≥ t$

I understand why this works but I am not sure how to prove it mathematically. It makes sense, because vertices of degree one are those at the end of each leaf (let their number be n) and/or the vertex in the beginning of the tree that doesn't branch into more than one edge. And the vertex with highest degree is gonna have at max n edges connected to it. Am I making sense? any help in the formal proof?