Is this (tricky) natural deduction with De Morgan's laws correct? Just a practice question, however just wondering if this natural deduction  proof is correct?
I have put brackets in 2.2 and not in 2.3 however this shouldn't make a difference?


1. ¬(P∧Q)          [premise]
2.1. ¬(¬P∨¬Q)      [assumption]
2.2.1. ¬P          [assumption]
2.2.2. ¬P∨¬Q       [∨intro 2.2.1]
2.2. ¬P→(¬P∨¬Q)    [→intro 2.2.1-2.2.2]
2.3.1. ¬P          [assumption]
2.3.2. ¬(¬P∨¬Q)    [restate 2.1]
2.3. ¬P→¬(¬P∨¬Q)   [→intro 2.3.1-2.3.2]
2.4. P             [RAA 2.2 2.3]
2.5.1. ¬Q          [assumption]
2.5.2. ¬P∨¬Q       [∨intro 2.5.1]
2.5. ¬Q→(¬P∨¬Q)    [→intro 2.5.1-2.5.2]
2.6.1. ¬Q          [assumption]
2.6.2. ¬(¬P∨¬Q)    [restate 2.1]
2.6. ¬Q→¬(¬P∨¬Q)   [→intro 2.6.1-2.6.2]
2.7. Q             [RAA 2.5 2.6]
2.8. P∧Q           [∧intro 2.4 2.7]
2. ¬(¬P∨¬Q)→(P∧Q)  [→intro 2.1-2.8]
3.1. ¬(¬P∨¬Q)      [assumption]
3.2. ¬(P∧Q)        [restate 1]
3. ¬(¬P∨¬Q)→¬(P∧Q) [→intro 2.1-2.8]
4. ¬P∨¬Q           [RAA 2 3]

