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. If  is true, and if  is true, then one may infer that  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:

where the rule is that wherever instances of "" and "" appear on lines of a proof, "" can validly be placed on a subsequent line.

Formal notation 
The biconditional introduction rule may be written in sequent notation:

where  is a metalogical symbol meaning that  is a syntactic consequence when  and  are both in a proof;

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

where , and  are propositions expressed in some formal system.

References

Rules of inference
Theorems in propositional logic