Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible.

~ = negation
& = conjunction
v = disjunction
| = line in a subproof

Here's what I have:

1. A - Premise
2. |~A - Assume
3. |~B - Assume
4. |~A&~B - &Intro;3.4
5. ~(~A&~B) - ~Intro;4

I'm quite sure this is wrong but I don't know how to fix it. Any help, even advice or tips, would be greatly appreciated!

• You have not discharged the two additional assumptions 2 and 3. Commented Feb 3, 2020 at 8:19
• You have to start with premise A and with assumption (~A&~B). Commented Feb 3, 2020 at 8:20
• I'm confused by how you can assume ~A when you have A as a premise. Also, don't you want to distribute ~ into the bracket? en.wikipedia.org/wiki/Negation#Distributivity en.wikipedia.org/wiki/De_Morgan%27s_laws Commented Feb 3, 2020 at 21:09
• @puppetsock You may assume anything you wish for the sake of an argument. However, it is not useful to assume ~A. Commented Feb 4, 2020 at 3:05
• If the answer below is enough for you, please accept it and we can "close" the post. Commented Feb 21, 2020 at 10:27

Negation introduction works by deriving a contradiction when assuming a position (`~A & ~B`), and thusly inferring its negation (`~(~A & ~B)`) holds when that assumption is discharged.
``````  |_ A            premise