Constructing Proofs for DeMorgan's Theorem using Basic Logical Rules

[ghosttea]

For my logic homework, I'm supposed to construct two proofs to prove that DeMorgan's is redundant. I'm not given a theorem or anything to start with.

I'm only allowed to use Modus Ponens, Modus Tollens, Hypothetical Syllogism, Simplification, COnjunction, Dilemma, Disjunctive Syllogism, Addition, Double Negation, Duplication, Commutation, Contraposition, Association, Biconditional Exchange, Conditional Exchange, Distribution, Exportation, Indirect Proof, and Conditional Proof.

Those are the only ones that we've studied in my class and the only ones that (I've noticed at least) are in the textbook (Understanding Symbolic Logic by Virginia Klenk). I'm only allowed to use Klenk's system, too.

I THINK I have one of them already, but I'm not completely positive. It feels... not quite right, but not quite wrong to me either.
1. ~A&B prem.
2. | (AvB) Assp. for I.P.
3. | ~A Simp. 1
4. | ~B Simp. 1
5. | A 2, 4 Disjunctive Syllogism
6. | (~A&A) 3, 5 conjunction
7. ~(AvB) 2-6 I.P.

I've tried looking around at the other answers for this on this forum, but none of them work for what I'm allowed to do.

 

[Nino MMP]

Any help would be appreciated. Here is another proof I constructed:1. ~A & B Premise2. | (AvB) Assumption for IP3. | A Assumption for IP4. | B Assumption for IP5. | ~(~A & B) 2,3 Conjunction6. ~(AvB) 1-5 IP I believe this is valid, but if someone could verify or provide feedback that would be wonderful. Thank you.