Derivation help please!!!

Question

I'm racking my brains out trying to remember!!!!!!! It looks so simple but I'm totally lost??? please help!!!

(Ǝx)Rx

answer:(Ǝx)(Rx v Dx)

Answer 1

Begin your proof by creating a subproof with a goal of Existential Elimination:

1 |_ (Ex)Rx Premise

2 | |_ Ra Assumption

Then, you create the disjunction needed for your conclusion:

1 |_ (Ex)Rx Premise

2 | |_ Ra Assumption

3 | | (Ra v Da) 2 vI

Next, you add on the existential operator to the disjunction:

1 |_ (Ex)Rx Premise

2 | |_ Ra Assumption

3 | | (Ra v Da) 2 vI

4 | | (Ex)(Rx v Dx) 3 EI

Finally (and importantly), you discharge the subproof to get your conclusion:

1 |_ (Ex)Rx Premise

2 | |_ Ra Assumption

3 | | (Ra v Da) 2 vI

4 | | (Ex)(Rx v Dx) 3 EI

5 | (Ex)(Rx v Dx) 1,2-4 EE

I hope this helps!