Rules of replacement

Double Negation (D. N.)

p = ~~p

Duplication (Dup.)

p = p p p = p p Commutation (Comm.)

p q = q p p q = q p

Association (Assoc.)

(p (q r)) = ((p q) r) (p (q r)) = ((p q) r)

Transposition (Trans.)

p q = ~q ~p DeMorgan's (DeM.)

~(p q) = ~p ~q ~(p q) =~p ~q Distribution (Dist.)

p (q r) = (p q) (p r) p (q r) = (p q) (p r) Exportation (Exp.)

(p q) r = p (q r) Material implication (impl).

p q = ~p q

Biconditional Exchange (B. E.)

p q = (p q) (q p)

Tautology (Taut).

p = p p p = p.p