Choose a minimum feedback edge set $F$ and one endpoint of each edge in $F$. The set $S$ of chosen endpoints has cardinality at most $|F|$. Every edge of the induced graph $G[V\setminus S]$ remains in $G-F$, so this induced graph is acyclic. Thus $S$ is a feedback vertex set and $\operatorname{FVN}(G)\leq |S|\leq |F|=\operatorname{FEN}(G)$.