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### 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL

#### [basic rules used in proofs of propositional logic]

14 ideas
 9394 MPP: Given A and A→B, we may derive B [Lemmon]
 9400 ∨I: Given either A or B separately, we may derive A∨B [Lemmon]
 9396 DN: Given A, we may derive ¬¬A [Lemmon]
 9397 CP: Given a proof of B from A as assumption, we may derive A→B [Lemmon]
 9398 ∧I: Given A and B, we may derive A∧B [Lemmon]
 9399 ∧E: Given A∧B, we may derive either A or B separately [Lemmon]
 9401 ∨E: Derive C from A∨B, if C can be derived both from A and from B [Lemmon]
 9402 RAA: If assuming A will prove B∧¬B, then derive ¬A [Lemmon]
 9395 MTT: Given ¬B and A→B, we derive ¬A [Lemmon]
 9393 A: we may assume any proposition at any stage [Lemmon]
 13500 Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD]
 14273 Conditional Proof is only valid if we accept the truth-functional reading of 'if' [Edgington]