Theorem 4exmid

The disjunction of the four possible combinations of two wffs and their negations is always true. A four-way excluded middle (see exmid ). (Contributed by David Abernethy, 28-Jan-2014.) (Proof shortened by NM, 29-Oct-2021.)

Conclusion
\( \vdash \varphi \wedge \psi \vee \neg \varphi \wedge \neg \psi \vee (\varphi \wedge \neg \psi \vee \psi \wedge \neg \varphi) \)
Proof
pm5.24
biimpi _
orri _