This rule can only be applied backwards to prove a FOR ALL formula containing an IMPLIES formula as its sub formula in one step, by declaring a skolem constant and assuming the LHS of the IMPLIES formula in a box with the RHS of the IMPLIES formula as its goal. <<<<<<< .mine

To apply this rule: =======

To use it backwards: >>>>>>> .r212

1. select both the FOR ALL IMPLIES goal line you wish to use and For All Arrow Introduction.
2. a new box will be added to your proof which declares a skolem term and assumes the LHS of the IMPLIES formula with the RHS as its goal, both after substituting the skolem term from the variable.
3. several FOR ALL can be dealt with at once.