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- ∧I
- - A
- - B
- - ⊦ A ∧ B
- ∧E
- - A ∧ B
- - ⊦ A
- ∨I
- - A
- - ⊦ A ∨ B
- ∨E
- - A → C
- - B → C
- - A ∨ B
- - ⊦ C
- →I
- - if (premises, A ⊦ B)
- - then (premises ⊦ A → B)
- →E
- - A
- - A → B
- - ⊦ B
- ¬I
- - A → B
- - A → ¬B
- - ⊦ ¬A
- ¬E
- - ¬A → B
- - ¬A → ¬B
- - ⊦ A
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