logical arguments

Modus Ponens p → q p ∴ q Modus Tollens p → q ~q ∴ ~p Generalization A) p ∴ p v q B) q ∴ p v q Specialization A) p ^ q ∴ p B) p ^ q ∴ q Conjunction p q ∴ p ^ q Elimination A) p v q ~q ∴ p B) p v q ~p ∴ q Transitivity p → q q → r ∴ p → r Proof by Division into Cases p v q p → r q → r ∴ r Contradiction Rule ~p → c ∴ p