Result on D41: Indicator function
Binary product of indicator functions equals indicator of intersection

Let $X$ be a D11: Set such that
 (i) $A, B \subseteq X$ are each a D78: Subset of $X$
Then $$I_A I_B = I_{A \cap B}$$
Proofs

Let $X$ be a D11: Set such that
 (i) $A, B \subseteq X$ are each a D78: Subset of $X$
This result is a particular case of R1193: Finite product of indicator functions equals indicator of intersection. $\square$