Full Idea
We write 'P if and only if Q' as P↔Q. It is called the 'biconditional', often abbreviate in writing as 'iff'. It also says that P is both sufficient and necessary for Q, and may be written out in full as (P→Q)∧(Q→P).
Gist of Idea
We write 'P if and only if Q' as P↔Q; it is also P iff Q, or (P→Q)∧(Q→P)
Source
E.J. Lemmon (Beginning Logic [1965], 1.4)
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.29
A Reaction
If this symbol is found in a sequence, the first move in a proof is to expand it to the full version.