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Aug 30, 2012 at 14:08 comment added Todd Trimble @Patricia: no problem!
Aug 30, 2012 at 13:47 comment added Patricia Hersh +1 for taking the time to figure out what was wrong with my suggestion, in addition to giving a proof.
Aug 30, 2012 at 5:33 comment added Colin Reid Yes, this is exactly the sort of proof I was looking for.
Aug 30, 2012 at 5:28 vote accept Colin Reid
Aug 30, 2012 at 2:06 comment added Todd Trimble If it helps at all, the iff condition says precisely that a Boolean algebra is a Heyting algebra for which $p \to q = \neg p \vee q$. I'm sure this must be in thousands of places, but see for example: en.wikipedia.org/wiki/Heyting_algebra#Examples
Aug 30, 2012 at 1:34 history edited Todd Trimble CC BY-SA 3.0
added 226 characters in body; deleted 106 characters in body
Aug 30, 2012 at 1:28 history answered Todd Trimble CC BY-SA 3.0