Let $G$ be a graph, and $P$ be the longest path in $G$. Let $x$ and $y$ be the start and end vertices of $P$ and let $m$ be the length of $P$. Prove that $deg(x)\le m$ and $deg(y)\le m$ for any graph $G$.
I can see why this is the case, but I am having trouble writing a proof for this. I am currently attempting this with proof by contradiction but am having trouble coming up with a generic way to show this.
How could I word this proof?