1
Q
MP
A
p→q, p ∴ q
2
Q
MT
A
p→q, ~q ∴ ~p
3
Q
DS
A
p∨q, ~p ∴ q (OR) p∨q, ~q ∴ p
4
Q
Simp
A
p∙q ∴ p or q
5
Q
Conj
A
p, q ∴ (p∙q)
6
Q
HS
A
p→q, (q→r) ∴ (p→r)
7
Q
Add
A
p ∴ p∨q (OR) p ∴ q∨p
8
Q
CD
A
p∨q, p→r, q→s ∴ r∨s
9
Q
DN
A
p :: ~~p
10
Q
EX
A
(p∙q)→r :: p→(q→r)
11
Q
Com
A
p∙q :: q∙p (OR) p∨q :: q∨p
12
Q
Dist
A
p∙(q∨r) :: (p∙q)∨(p∙r)
13
Q
Dist
A
p∨(q∙r):: (p∨q)∙(p∨r)
14
Q
As
A
p∨(q∨r) :: (p∨q)∨r
15
Q
As
A
p∙(q∙r) :: (p∙q)∙r
16
Q
Re
A
p :: p∙p (OR) p ::p∨p
17
Q
DeM
A
~(p∙q) :: ~p∨~q (OR) ~(p∨q) :: ~p∙~q
18
Q
ME
A
p↔q :: (p→q)∙(q→p)
19
Q
ME
A
p↔q :: (p∙q)∨(~p∙~q)
20
Q
Cont
A
p→q :: ~q→~p
21
Q
MI
A
p→q :: ~p∨q
Phil 102
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