Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional is true. For example, if it's true that I'm breathing if and only if I'm alive, then it's true that if I'm breathing, I'm alive; likewise, it's true that if I'm alive, I'm breathing. The rules can be stated formally as:

and

" can be placed on a subsequent line.

Formal notation

The biconditional elimination rule may be written in sequent notation:

and

is a metalogical in the other are syntactic consequences in some logical system;

or as the statement of a truth-functional tautology or theorem of propositional logic:

are propositions expressed in some formal system.

See also

• Logical biconditional

References