Discrete Mathematics - Rules of Inference

p
p → q
∴ q

Modus Ponens

¬q
p → q
∴ ¬p

Modus tollens

p → q
q → r
∴ p → r

transitivity

p ∨ q
¬p
∴ q

elimination

p
∴ p ∨ q

Generalization

p ∧ q
∴ p

Specialization

~p→ C
∴ p

Contradiction

p ∨ q
p → r

q → r
∴ r

proof by cases