Final version: posted Feb 5
Use Conditional Proof (and possibly the previous rules) to prove the following sequents. Be sure to include dependency numbers in the leftmost column of your proof.
P → Q ⊢ P → (Q∨R)
P → (Q→R) ⊢ Q → (P→R)
¬P ⊢ ¬(P∧Q)
¬(P∨Q) ⊢ ¬P
P ⊢ (P→¬P) → ¬P
P ⊢ ¬(P→¬P)
Use ∨-elimination (and possibly the previous rules) to prove the following sequents. Do not use reductio ad absurdum for any of these proofs.
P ∨ (Q∧R) ⊢ P ∨ Q
P ∧ (Q∨R) ⊢ (P∧Q) ∨ (P∧R)
P ∨ Q, ¬P ⊢ Q
(P→R) ∧ (Q→R) ⊢ (P∨Q) → R