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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!

2

No. Your subproof is drawkcab. You are not aiming to derive a position from a random assumption.

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.

And so ...

  |_ A            premise
  |  |_ ~A & ~B   assumption
  |  |  :         :
  |  |  #         ~ elimination
  |  ~(~A & ~B)   ~ introduction
| improve this answer | |

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