Rule do Application Explanation
Wedge Introduction do X 3 vI L X is the disjunct to be introduced, 3 is the line number to which Wedge Introduction needs to be applied and L denotes - introduce the argument X on left side. Similarly you can specify "do X 3 vI R" to introduce the argument on the Right side.
Wedge Elimination do 2, 4 vE 2,4 are the line numbers to which Wedge Elimination needs to be applied.
Ampersand Introduction do 5,6 &I R 5,6 are the line numbers to which Ampersand Introduction needs to be applied. L means place sentence at first listed line on left side of the junction; R means place it on the right.
Ampersand Elimination do 7 &E 7   is the line numbers to which Ampersand Elimination needs to be applied.
Arrow Introduction do 4->I(2) 2,4 are the line numbers to which Arrow Introduction needs to be applied.
Arrow Elimination do 7,10 ->E 7,10 are the line numbers to which Arrow Elimination needs to be applied.
Biconditional Introduction do 3,5 <->I L 3,5 are the line numbers to which Biconditional Introduction needs to be applied, L or R to swap the arguments on either side of the biconditional.You can use "do 3,5 <->I R" to swap the arguments
Biconditional Elimination do 4 <->E R 4 is the line number to which Biconditional Elimination needs to be applied, R - conditional statement with right side one as antencedent and left one as consequent. Similarly you can use "do 4 <->E L" to form conditional statement with left side one as antecedent and right side one as consequent.

 

e.g. proofs :

PvQ->R, P, @xFx, Fa&R->S |- S

 P->Q, Q->R |- P->R
   
1 (1) PvQ->R A
2 (2) P A
do Q 2vI R
do 1,3 ->E
5 (5) @xFx A
5 (6) Fa 5 @E
do 4,6 &I R
8 (8) Fa&R->S A
do 7,8 ->E		 1 (1) P->Q A
2 (2) Q->R A
3 (3) P A
do 1,3 ->E
do 2,4 ->E
do 5->I(3)