Let $M_X = (X, \mathcal{F}_X)$ and $M_Y = (Y, \mathcal{F}_Y)$ each be a D1108: Measurable space such that

(i)	$f : X \to Y$ is a D1519: Constant map from $X$ to $Y$

Let $\sigma_{\text{pullback}} \langle f \rangle$ be the D1730: Pullback sigma-algebra on $X$ under $f$ with respect to $M_Y$. Result R2548: Constant map pulls back a bottom sigma-algebra shows that $\sigma_{\text{pullback}} \langle f \rangle = \{ \emptyset, X \}$ and result R4651: Bottom sigma-algebra is always a subsigma-algebra shows that \begin{equation} \sigma_{\text{pullback}} \langle f \rangle = \{ \emptyset, X \} \subseteq \mathcal{F}_X \end{equation} This establishes the result. $\square$