Arrow Elimination
   
 

This rule can be used forwards to derive the right subformula of an IMPLIES formula from it's left, or backwards from the goal.

To use it forwards:
  1. select an empty line and Arrow Elimination.

  2. then select an IMPLIES formula and a formula the same as left sub formula. Both formulas must be in scope of empty line.

  3. the right subformula of the IMPLIES formula will then be added to your proof.
To use it backwards:
  1. select the goal line and Arrow Elimination.

  2. then select the IMPLIES formula line you wish to use for the elimination, which must be in the scope of the goal line.

  3. If the right side of the implies formula is the same as the goal formula, the left sub formula will be added to your proof as a new goal and if the right side is not the same then two proof lines will be added above the existing goal. The left sub formula of the implies formula will be a goal (other than the existing goal) and the right sub formula is added with justification arrow elimination.