1
Q
Permutation With Replacement
A
N^K
2
Q
Combination with replacement
A
C(n+k-1,k)
3
Q
P->q
q-> r
Line
therefore p->r
A
Hypothetical Syllogism
4
Q
P->q
P
Line
Therefore Q
A
Modus Ponens
5
Q
P->q
Not Q
Line
Therefore not P
A
Modus tollens
6
Q
P or Q
Not p
Line
Therefore Q
A
Disjunctive
7
Q
P or Q
Not p
Line
Therefore Q
A
Disjunctive Syllogism
8
Q
P
Line
P or Q
A
Additiom
9
Q
P and q
Line
P
A
Simplification
10
Q
P
Q
Line
P and Q
A
Conjunction
11
Q
For Allx P(x)
Line
P(c)
A
Universal Instantiation
12
Q
P(C) for an arbitrary c
Line
For allx p(x)
A
Universal Generalisation
13
Q
A
14
Q
Conditional Disjunctive
A
P->q = not p or q
15
Q
Biconditional
A
P <->q = (p->q) and (q->p)
