praeclarum theorema
The praeclarum theorema, or splendid theorem, is a theorem of propositional calculus^{} that was noted and named by G.W. Leibniz, who stated and proved it in the following manner:
If $a$ is $b$ and $d$ is $c$, then $ad$ will be $bc$.
This is a fine theorem, which is proved in this way:
$a$ is $b$, therefore $ad$ is $bd$ (by what precedes),
$d$ is $c$, therefore $bd$ is $bc$ (again by what precedes),
$ad$ is $bd$, and $bd$ is $bc$, therefore $ad$ is $bc$. Q.E.D.
(Leibniz, Logical Papers, p. 41).
Expressed in contemporary logical notation, the praeclarum theorema (PT) may be written as follows:
$$((a\Rightarrow b)\wedge (d\Rightarrow c))\Rightarrow ((a\wedge d)\Rightarrow (b\wedge c))$$ 
Representing propositions^{} (http://planetmath.org/PropositionalCalculus) as logical graphs (http://planetmath.org/LogicalGraph) under the existential interpretation^{} (http://planetmath.org/LogicalGraphFormalDevelopment), the praeclarum theorema is expressed by means of the following formal equation:
(1) 
And here’s a neat proof of that nice theorem.
(2) 
1 References

•
Leibniz, Gottfried W. (1679–1686 ?), “Addenda to the Specimen of the Universal^{} Calculus”, pp. 40–46 in G.H.R. Parkinson (ed., trans., 1966), Leibniz : Logical Papers, Oxford University Press, London, UK.
2 Readings

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Sowa, John F. (2002), “Peirce’s Rules of Inference^{}”, http://www.jfsowa.com/peirce/infrules.htmOnline.
3 Resources

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Dau, Frithjof (2008), http://web.archive.org/web/20070706192257/http://drdau.net/pc.shtmlComputer Animated Proof of Leibniz’s Praeclarum Theorema.

•
Megill, Norman (2008), http://us.metamath.org/mpegif/prth.htmlPraeclarum Theorema @ http://us.metamath.org/mpegif/mmset.htmlMetamath Proof Explorer.
Title  praeclarum theorema 
Canonical name  PraeclarumTheorema 
Date of creation  20130322 17:47:37 
Last modified on  20130322 17:47:37 
Owner  Jon Awbrey (15246) 
Last modified by  Jon Awbrey (15246) 
Numerical id  16 
Author  Jon Awbrey (15246) 
Entry type  Theorem 
Classification  msc 03B70 
Classification  msc 03B35 
Classification  msc 03B22 
Classification  msc 03B05 
Classification  msc 0303 
Classification  msc 01A45 
Synonym  splendid theorem 
Related topic  OrderedGroup 