This rule when used forwards creates a new box with a new name replacing the exists variable, to prove a goal which is taken as input and when used backwards creates a new box and a new name replacing the exists variable, to prove the goal.

To use it forwards:

1. select both the empty line and Exists Elimination.
2. then enter the goal you wish to prove by Exists Elimination. This formula must not contain any predicate symbols, function symbols or constants that are not in the signature of the box you are working in.
3. a new box will then be added to your proof declaring a skolem term and assuming the sub formula of the EXISTS formula with the skolem term replacing the EXISTS variable. The conclusion of the box is set to the goal formula that was taken as input.
4. if a formula is prefixed by more than one EXISTS there is an option to eliminate them all rather than just the first one.

1. select both the goal line you want to prove using the rule and Exists Elimination.
2. then select the EXISTS formula you wish to eliminate to prove this goal (this line must be in the scope of the goal line).
3. a new box will then be added to your proof declaring a skolem term and assuming the sub formula of the THERE EXISTS formula with the skolem term replacing the EXISTS variable. The conclusion of the box is set the goal formula you selected.
4. if a formula is prefixed by more than one EXISTS there is an option to eliminate them all rather than just the first one.