Biconditional Introduction

Proof Rule
The rule of biconditional introduction is a valid deduction sequent in propositional logic: If we can conclude both $p \implies q$ and $q \implies p$, then we may infer $p \iff q$.

It can be written:
 * $\displaystyle {\displaystyle {{p \implies q} \atop {q \implies p}} \over p \iff q} \iff_i$

Thus it is used to introduce the biconditional operator into a sequent.

Technical Note
When invoking Biconditional Introduction in a tableau proof, use the BiconditionalIntro template:



or:

where:
 * is the number of the line on the tableau proof where Biconditional Introduction is to be invoked
 * is the combined pool of assumptions of each of the constituents (comma-separated list)
 * is the statement of logic that is to be displayed in the Formula column, without the  delimiters
 * is the first of the two lines of the tableau proof upon which this line directly depends
 * is the second of the two lines of the tableau proof upon which this line directly depends
 * is the (optional) comment that is to be displayed in the Notes column.

Also known as
Some sources refer to this is the rule of Conditional-Biconditional.