Thenn is a rarely used but quite spiffy shorthand for "then and only then". It is modeled after the much more popular iff, meaning "if and only if".

In propositional logic the English words 'if' and 'then' are used to express the operator implication: "if X then Y" (X → Y). Likewise, the operator logical equivalence may be expressed as "if X then Y, and if Y then X" (X ↔ Y). In order to avoid saying all of this, many people will simply write "X iff Y". And some very special people will go so far as to write "iff X thenn Y". Of course, since iff and thenn are pronounced the same as if and then, these words are really only useful in written language. Although if you are sufficiently geeky you can always pronounce them "if-ef" and "then-en".

In practice, thenn is simply a rhetorical flourish intended to ease the introduction of logical stringency into everyday speech. It is usually used when the writer wants to avoid using if/iff for some reason -- generally to preserve the flow of natural language, i.e. "When this is backed up with verifiably correct reasoning, thenn will I agree." Obviously, if you are using thenn to perserve the natural flow of language, you are a dork.

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