British Dictionary definitions for material-equivalence
equivalence
/ɪˈkwɪvələns/
noun
1.
the state of being equivalent or interchangeable
2.
(maths, logic)
the relationship between two statements, each of which implies the other
Also called biconditional. the binary truth-function that takes the value true when both component sentences are true or when both are false, corresponding to English if and only if. Symbol: ≡ or ↔, as in –(p ∧ q) ≡ –p ∨ –q
in logic and mathematics, the formation of a proposition from two others which are linked by the phrase "if, and only if." The equivalence formed from two propositions p and q also may be defined by the statement "p is a necessary and sufficient condition for q."