IFF Introduction
   
 

This rule is used to introduce an if and only if formula from two opposite implies formulas (a -> b and
b -> a can be used to get a # b), or backwards to split an if and only if formula up into two boxes to prove left ARROW right and right ARROW left. <<<<<<< .mine

To use it forwards: =======

To use it forwards: >>>>>>> .r212

  1. select both an empty line and IFF Introduction.
  2. select two opposite implies lines (for example a -> b and b -> a), which are in the empty line's scope. The left and right hand sides of the IF AND ONLY IF formula will be the same as the left and right sides of the first ARROW formulas selected here.
  3. this will add the IF AND ONLY IF formula line to the proof.

To use it backwards:

  1. select both the IF AND ONLY IF goal line and IFF Introduction.
  2. This will add two new boxes to the proof which are used to prove the left side IMPLIES right side of the IFF formula and the right side IMPLIES the left side.