All the Derivation Rules of SD and

Rules of Inference

Modus Tollens (MT)

PQ
Q
P

Hypothetical Syllogism (HS)

PQ
QR
PR

Disjunctive Syllogism (DS)

PQ
P
Q
or
PQ
Q
P

Rules of Replacement

Commutation (Com)

P&Q⊲⊳Q&P
PQ⊲⊳QP

Association (Assoc)

P&(Q&R)⊲⊳(P&Q)&R
P(QR)⊲⊳(PQ)R

Implication (Impl)

PQ⊲⊳PQ

Double Negation (DN)

P⊲⊳∼∼P

De Morgan (DeM)

(P&Q)⊲⊳PQ
(PQ)⊲⊳P&Q

Idempotence (Idem)

P⊲⊳P&P
P⊲⊳PP

Transposition (Trans)

PQ⊲⊳QP

Exportation (Exp)

P(QR)⊲⊳(P&Q)R

Distribution (Dist)

P&(QR)⊲⊳(P&Q)(P&R)
P(Q&R)⊲⊳(PQ)&(PR)

Equivalence (Equiv)

PQ⊲⊳(PQ)&(QP)
PQ⊲⊳(P&Q)(P&Q)