Rules of inference
Conjunction
and-introduction
adjunction
conjunction introduction
and-elimination
Disjunction
Disjunction introduction
β¨I
Disjunction elimination, β¨EL and β¨ER
implication
(modus ponens, implies-elimination, arrow-elimination)
implication introduction
implication elimination (modus ponens, implies-elimination, conditional elimination)
conditional proof (conditional introduction)
modus tollens
Modus ponens
Negation
Negation introduction (Reductio ad absurdum)
double negation
De Morgan's laws
The negation of conjunction rule may be written in sequent notation:
The negation of disjunction rule may be written as:
De Morgan's duality can be generalised to quantifiers, the universal quantifier and existential quantifier are duals:
Rules of propositional calculus
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