RULE OF INFERENCE AND REPLACEMENT:  and ≡
A conditional asserts that the truth of one claim (the antecedent) forces
the truth of the other (the consequent). As a result, if we know that the
antecedent is true, then we also know that the consequent is true (Modus
Ponens). In addition, since the truth of the antecedent forces the truth of
the consequent, if we know that the consequent is false, we know that the
antecedent must also be false (Modus Tollens).
MODUS PONENS
Given p ‫ כ‬q and p
MODUS TOLLENS
Given p ‫ כ‬q and ~q
we can deduce q
we can deduce ~p
HYPOTHETICAL SYLLOGISM
Given p ‫ כ‬q and q ‫ כ‬r
CONSTRUCTIVE DILEMMA
Given p V q and p ‫ כ‬r and
q‫כ‬s
we can deduce p ‫ כ‬r
we can deduce r V s
RULES OF REPLACEMENT:  and ≡
TRANSPOSITION
The formula p ‫ כ‬q
EXPORTATION
The formula (p & q) ‫ כ‬r
can (1) replace or can (2)
be replaced at any time
during a deduction by
can (1) replace or can (2)
be replaced at any time
during a deduction by
~q ‫~ כ‬p.
p ‫( כ‬q. ‫ כ‬r)
(modus tollens)
IMPLICATION
The formula p ‫ כ‬q
EQUIVALENCE
The formula p ≡ q
can (1) replace or can (2)
be replaced at any time
during a deduction by
can (1) replace or can (2)
be replaced at any time
during a deduction by
~p V q
(p ‫ כ‬q) & (q ‫ כ‬p)
and (p &q) V (~p & ~q)