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This axiom is also called "T suf", and like its relative (p>q) > ((r>p)>(r>q)) ("T pre") in the presence of Uniform Substitution and detachment (for >) they yield the rule if |- p>q and |- q>r infer |- p>r . [Chidgey, 1973, page 273]

In the presence of either of the rules:

- From |- p > (q>r) infer |- q > (p>r)
- From |- p > ((q>r)>s) infer |- (q>r) > (r>s)

Or the axiom:

- p > ((p>q) > q)

T pre and T suf are equivalent. (And not in a whole of other cases -JH) [Chidgey, 1973, page 273]

© Copyright 2007 by John Halleck, All Rights Reserved. This page is http://www.cc.utah.edu/~nahaj/logic/structures/axioms/CCpqCCqrCpr.html This page was last modified on January 22nd, 2007.