Philosophical Propositional Calculus (0)

Derivation Rules:

Reiteration (R) In a proof, a previously established result can always be stated again.
P
P

Conjunction Elimination (∧E) When two statements are conjoined each component can be stated seperately.
P ∧ Q            P ∧ Q
P                   Q

Conjunction Introduction (∧I) Two seperate results can always be conjoined as a conjunction.
P
Q
P ∧ Q

Disjunction Introduction (∨I) For any result P, P or some other statement is always true.
P                      P
P ∨ Q               Q ∨ P

Conditional Elimination (⇒E) The rule of Modus Ponens (MP)
P ⇒ Q
P
Q

Biconditional Elimination (⇔E) If two statements are equivalent and either is true, then the other must too be true.
P ⇔ Q               P ⇔ Q
P                        Q
Q                        P