From Jech's Set Theory:
Exercise (2.3). If $X$ is inductive, then $X\cap\text{Ord}$ is inductive. $\textbf{N}$ is the least nonzero limit ordinal, where $\textbf{N} = \bigcap\{X:X\text{ is inductive}\}$.
I'm struggling to prove the second statement; specifically that $\textbf{N}$ is transitive (already know it is a woset), which is needed to show it is an ordinal.
I'd appreciate any hints.