If S is a subspace of a vector space V, then S is a vector space.

De Morgan's Laws:

$\displaystyle P\rightarrow Q\equiv P \wedge \sim Q$

Assume S isn't a vector space and since S is a subspace of V, then $\displaystyle S\subseteq V$.

Since S isn't a vector space, it follows that V isn't a vector space. However, V is a vector space; therefore, by contradiction, S is a vector space.

Correct?