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.