Arrow Introduction
   
 

This rule can be used both forwards and backwards to derive an IMPLIES formula as result either on an empty line or as a goal.
When done so a proof box is formed in which the assumation is the LHS of the IMPLIES formula and the goal is the RHS.

To use this rule forwards:
  1. select both an empty line and IMPLIES Introduction (Arrow Introduction); this will provide an Input Box
    that asks you for the IMPLIES formula that is to be derived as a goal.

  2. enter the IMPLIES formula to be derived; this will create a box with the LHS of the IMPLIES formula an assumption and the RHS of the IMPLIES formula as goal. The IMPLIES formula must not contain any predicate symbols, function symbols or constants that are not in the signature of the box you are working in.

To use this rule backwards:
  1. select both a goal line (which must be an IMPLIES formula) and IMPLIES Introduction (Arrow Introduction)

  2. this will add a new box to your proof with the left hand side of the IMPLIES formula as its assumption and the IMPLIES formula's RHS as its goal.