The Nine Rules of Inference
The nine rules of inference are all valid elementary argument forms (which can be easily proved to be valid by truth tables).

The point of the distinction between "rules of inference" and "rules of replacement" is that rules of inference may only be applied to lines in a proof in which the whole line has the form of the premiss in that argument form.  We express this by saying that rules of inference cannot be applied to parts of a line.  In contrast, rules of replacement are not so restricted; they may be applied to parts of a line.

The nine rules below must all be memorized precisely:

Modus Ponens (M.P.)

Modus Tollens (M.T.)

Hypothetical Syllogism (H.S.)

Disjunctive Syllogism (D.S.)

Conjunction (Conj.)

Simplification (Simp)

Addition (Add)

Constructive Dilemma (C.D.)

Destructive Dilemma (D.D.)