ThmDex – An index of mathematical definitions, results, and conjectures.
Proof P3476 on R2164: Law of the excluded middle in probability calculus
P3476
Using result R977: Ambient set is union of subset and complement of subset, we have \begin{equation} \mathbb{P}(E \cup E^{\complement}) = \mathbb{P}(\Omega) = 1 \end{equation} $\square$