This video covers the following implication rules for propositional logic natural deduction: Simplification (Simp), Conjunction (Conj), Addition (Add), and Constructive Dilemma (CD)
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I suppose that one elegant proof to 01:07:45 might be as follows: - ... 5. !K 4 simp 6. L v !M 3, 5 MP 7. J v !O 2, 6 CD 8. K v !P 1, 7,CD 9. !P 5, 8 DS
