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I would count it as jargon and I'd never use it in prose. It's a programming/maths term meaning if and only if and should be restricted to circles where it's likely to be understood (edit like XKCD ).
The question of whether it's an abbreviation is interesting. It's obviously shorter than "if and only if" but I think I'd say it was a more of a symbol. Perhaps that's my programming background coming out [where symbol has a particular meaning (see number 2 here)]. However as it consists of more than one recognisable letter, it might be better to say it's an abbreviation
Here's an Ngram which shows that iff has become more popular recently, corresponding to the increase in computing. That may explain the increase in "if and only if" as well. I have no idea whether the incidence around 1800 is simply an alternative spelling of if or whether that actually meant "if and only if".
Personally, I don't really care if it's listed or not.
IFF is, as far as I know, an established contraction of if and only if in engineering, physics, philosophy (I believe the first experience I had with IFF was when our philosophy professor used it), and as I recall in mathematics as well. Some people are snarky about it, some aren't. I use it all the time. I've seen it used in all the areas above over the past three or four decades.
Perhaps not definitively a "word" in the spoken sense. but a "working" word or defacto written word? Yes, pretty much.
Re: is iff a word, or an abbreviation?
Does it need to be one or the other? It doesn't seem to be either one, in a pure sense.
I'm more comfortable identifying it as shorthand for "if and only if".
Dictionaries specifically relate the word shorthand to the standardized system of stenography, but many also list a secondary definition, something along the lines of "an abbreviated or shortened way of communicating something."
Wear the shoe iff it fits... In this case, I think shorthand fits better than either abbreviation or word.
While acknowledging the excellent answer from @Andrew Leach, one man's jargon is another man's specialized terminology. To the non-mathematician, this is jargon. To the logician, this is an abbreviation that is used in a similar way (though not as frequently) as QED. (At the bottom of a proof, a mathematician will write QED, standing for quod erat demonstrandum, to indicate that he or she has proven that which was set out to be proven.) You may find QED in popular usage, but it is both specialized terminology and an abbreviation.
I first ran across IFF in my 8th grade algebra class, and it was used in logic truth tables. It meant, as others have correctly stated, "If-and-only-if."
In the context of the XKCD comic, it means Honk if (and only if) you love formal logic. The truth table would be:
This means that if you honk because the driver swerved into your lane, then you are not obeying the bumper sticker (or the truth value of the bumper sticker's logical statement). And if you don't honk even though you love formal logic, then you're not obeying the truth value of the bumper sticker.
My experience in both programming and math has seen IFF rarely in programming and sometimes in math and logic. Few programmers, for instance, would recognize the equivalence between ~ XOR (not Exclusive OR operation) and IFF.
Q.E.D., but IFF you understood the truth table.
OED 1971 doesn't list iff at all. The American Heritage Dictionary of the English Language, Fourth Edition says it's an abbreviation. Difficult to consider it a real word when it's normally pronounced as three separate letters.