This rule allows you to introduce an exists formula into your proof from a formula you have already shown (usually containing a closed term you substitute the new exists variable for), or when used backwards allows to get a new goal line (see below) by substituting the variable in it for a closed term (that is already in the signature).
To use this rule forwards:

1. select both an empty line and Exists Introduction
2. select a formula line in the scope of the empty line usually containing a non-variable (closed) term.
3. If you have multiple instances of the term in the formula then you can replace either all instances of the term or any one of them:
   1. To replace a single instance of the term in the formula just enter the formula you wish to introduce as an Exists formula and it is added to your proof line
   2. To replace all instances of the term click OK and when promted enter the term you wish to replace and the Exists variable.
4. a new EXISTS line will then be added to the proof provided the values you entered in step 3 were valid.

(NOTE: This rule is slightly limited in that it does not allow, for example to derive EyEx[p(x,y)] from Ex[p(x,x)] even though this is valid.)

1. select both the EXISTS goal line and Exists Introduction.
2. when prompted enter the term you wish to substitute the variable for in the formula, this term must be in the goal line's signature.
3. a new goal line will be added to your proof consisting of the EXISTS formula's sub formula with the variable substituted by the term you entered.

(NOTE: In backwards mode you can deal with several EXISTS at once but not in forwards mode.)