Open subset of open subspace is open

Statement
Suppose $$X$$ is a topological space and $$V$$ is an open subset of $$X$$. Suppose $$U$$ is a subset of $$V$$ that is an open subset of $$V$$ under the subspace topology on $$V$$. Then, $$U$$ is also an open subset of $$X$$.

Related facts

 * Closed subset of closed subspace is closed
 * Dense subset of dense subspace is dense