Addition
If P is a premise, we can use Addiction rule to derive P ∨ Q.
Conjunction
If P and Q are two premises, we can use Conjunction rule to derive P ∧ Q.
Simplification
If P ∧ Q is a premise, we can use Simplification rule to derive P.
Modus Ponens
If P and P→Q are two premises, we can use Modus Ponens to derive Q.
Modus Tollens
If P→Q and ¬Q are two premises, we can use Modus Tollens to derive ¬P.
Disjunctive Syllogism
If ¬P and P ∨ Q are two premises, we can use Disjunctive Syllogism to derive Q.
Hypothetical Syllogism
If P→Q and Q→R are two premises, we can use Hypothetical Syllogism to derive P→R
Constructive Dilemma
If ( P→Q ) ∧ (R→S) and P ∨ R are two premises, we can use constructive dilemma to derive Q ∨ S.
Destructive Dilemma
If (P→Q) ∧ (R→S) and ¬Q ∨ ¬S are two premises, we can use destructive dilemma to derive P ∨ R.
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