Discrete mathematics: reasoning rules

Rules of reasoning	interpretative statement
Premise introduction rules	Premise can be introduced at any time of proof
Conclusion introduction rules	At any time of proof , The proved conclusion can be used as the premise of subsequent proof
Replacement rule	At any time of proof , Any sub propositional formula in a propositional formula can be replaced by an equivalent propositional formula
Hypothetical reasoning rules	P ∧ (P→Q) ⇒ Q
Additional rules	P ⇒ P∨Q
Simplify the rules	P ∧ Q ⇒ P
Rejection rule	¬Q∧(P→Q) ⇒ ¬P
Hypothetical syllogism rule	(P→Q)∧(Q→R) ⇒ P→R
Disjunctive syllogism rule	¬P∧(P∨Q) ⇒ Q
Constructive dilemma rule	(P∨Q)∧(P→R)∧(Q→S) ⇒ (S∨R)