This rule can be used forwards to derive either the left or right hand sub formula from an IF AND ONLY IF formula using the other sub formula, or backwards to derive one of the sub formulas as a new goal line using the other sub formula.
To use it forwards:

1. select both an empty line and If and Only If Elimination.
2. then select the IF AND ONLY IF formula you wish to eliminate and a formula which matches either the left or right sub formula of the the IF AND ONLY IF formula. Both the formulas must be in the scope of the empty line.
3. the sub formula on the other side of the IF AND ONLY IF formula from the formula you selected will then be added, as a new line, into your proof.

1. select both the goal line which matches a sub formula of the IF AND ONLY IF formula you wish to eliminate and If and Only If Elimination.
2. then select the IF AND ONLY IF formula you wish to use in the elimination, which must be in the scope of the goal line.
3. the sub formula on the other side of the IF AND ONLY IF formula from the goal formula will then be added as a new goal to your proof.