In propositional logic, biconditional introduction is a valid rule of inference. It allows for one to infer a biconditional from two conditional statements. The rule makes it possible to introduce a biconditional statement into a logical proof is true. For example, from the statements "if I'm breathing, then I'm alive" and "if I'm alive, then I'm breathing", it can be inferred that "I'm breathing if and only if I'm alive". Biconditional introduction is the converse of biconditional elimination. The rule can be stated formally as:

" can validly be placed on a subsequent line.

Formal notation

The biconditional introduction rule may be written in sequent notation:

is a metalogical is a syntactic consequence are both in a proof;

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

are propositions expressed in some formal system.

References