Full Idea
Two propositions are 'equivalent' if whenever A is true B is true, and whenever B is true A is true, in which case A↔B is a tautology.
Gist of Idea
Two propositions are 'equivalent' if they mirror one another's truth-value
Source
E.J. Lemmon (Beginning Logic [1965], 2.3)
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.70