I'm trying to prove the expression ¬¬A→A. I can use 3 axioms:
- A1: a→(b→a)
- A2: (a→(b→c))→((a→b)→(a→c))
- A3: (¬b→¬a)→(a→b),
MP rule and deduction theorem.
What am I doing wrong?
⊢ ¬¬A → A
¬¬A ⊢A deduction th.
1.¬¬A
2.¬¬A→(¬A→¬¬A) [A1]
3.¬A→¬¬A [MP(1,2)]
4.(¬A→¬¬A)→(¬A→A) [A3]
5.¬A→A [MP(3,4)]