Subspace topology is transitive

Statement
Suppose $$A \subset B \subset X$$, where $$(X, \tau)$$ is a topological space. Then, there are two ways to obtain a topology on $$A$$:


 * Take the subspace topology on $$A$$ coming from the topology $$\tau$$ on $$X$$
 * First, take the subspace topology on $$B$$ coming from the topology $$\tau$$ on $$X$$. Then, take the subspace topology on $$A$$ from this topology on $$B$$

Both these topologies on $$A$$ are the same.