Result on D41: Indicator function
Subresult to R1193: Finite product of indicator functions equals indicator of intersection
Binary product of indicator functions equals indicator of intersection
Formulation 0
Let $X$ be a D11: Set such that
(i) $A, B \subseteq X$ are each a D78: Subset of $X$
Then \begin{equation} I_A I_B = I_{A \cap B} \end{equation}
Proofs
Proof 0
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. $\square$