Proof strategy again

RULES 1- 12

1

ELIMINATION (ELIM):

GIVEN P or Q and not P, we may conclude Q.

2

AFFIRMING THE ANTECEDENT (MPP):

GIVEN if P then Q and P, we may conclude Q.

3

DENYING THE CONSEQUENT (MTT):

GIVEN if P then Q and not Q, we may conclude not P.

4

DOUBLE NEGATION (DN):

GIVEN not not P, we may conclude P, and vice versa.

5

'AND' INTRODUCTION (&I):

GIVEN P and Q, we may conclude P and Q

6

'AND' ELIMINATION (&E):

GIVEN P and Q, we may conclude P.

7

CHAIN RULE (CH):

GIVEN if P then Q and if Q then R, we may conclude if P then R.

8

DILEMMA (DIL):

GIVEN if P then R and if Q then R, we may conclude if (P or Q) then R.

9

CONTRAPOSITION (CONTRA):

GIVEN if P then Q, we may conclude if not Q then not P, and vice versa.

10

NEITHER/NOR RULE (NNOR):

GIVEN not P and not Q, we may conclude not (P or Q), and vice versa.

11

NOT-BOTH RULE (NAND):

GIVEN not P or not Q, we may conclude not (P and Q), and vice versa.

12

BICONDITIONAL RULE (IFF):

GIVEN P iff Q, we may conclude if P then Q and if Q then P, and vice versa.

('P or Q' is short for 'a statement of form P or Q' (etc.); and any statement whose form is a substitution instance of P or Q is a statement of form P or Q.)