+- MKLab (https://mklab.gr)
+-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1)
+--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3)
+---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13)
+---- Thread: Praeclarum theorema [Leibniz] (/showthread.php?tid=417)
Praeclarum theorema [Leibniz] - mklabgr - 06-16-2026
Summary
The Praeclarum Theorema (“splendid theorem”), introduced by Leibniz, is a basic result in propositional logic showing that implication distributes over conjunction: if $(a \Rightarrow b) and (d \Rightarrow c), then from (a \land d) one can conclude (b \land c)$. In other words, combining two separate logical implications allows one to combine their conclusions when their premises are both true.
The theorem is typically written in modern notation as $(((a \Rightarrow b) \land (d \Rightarrow c)) \Rightarrow ((a \land d) \Rightarrow (b \land c)))$, and it serves as an early example of structured reasoning in formal logic and is often illustrated using logical graphs or proof systems in foundational studies of logic.
ARTICLE
RE: Praeclarum theorema [Leibniz] - mklabgr - 06-16-2026
Jon Awbrey provides an explanation and proof of the Praeclarum Theorema, also known as the Splendid Theorem, which states:
ARTICLE