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- ∨E1
- - A ∨ B, ¬A ⊦ B
- ∨E2
- - A ∨ B, ¬B ⊦ A
- ¬E1
- - ¬¬A ⊦ A
- ¬E2
- - ¬A → B, A → B ⊦ B
- →I1
- - ¬A ⊦ A → B
- →I2
- - B ⊦ A → B
- →E1
- - A → B ⊦ ¬A ∨ B
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