Vectorspace subspace proof V is $n$ dimensional vectorspace over $\mathbb{R}$. $W\subset V$ is $m$ dimensional subspace over $\mathbb{R}$ and  $m < n$.
$$Y=\bigcap \{U:U \text{ is a subspace of} \ V, \dim U=n-1, W \subset U \}$$
Prove that $Y=W$.
I could use some help on this problem.

We have $W ⊂ Y$ trivially. Then note that you can extend a base of $W$ to a base of $V$ and leave out one of the adjoined base vectors to obtain a subspace $U ⊂ V$ of dimension $n-1$.
