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}

Result R4333
on D41: Indicator function

*Subresult of 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

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. $\square$