Symbolic Logic
Inference rules
MP
MT
H S.
(p ::J q)
(p ::J q)
P
-q
(p ::J q)
(q::J r)
I ... q
I ... -p
~
p
q
D.S.
-------­
I ... (p
e
q)
lliJ
(p ::J q)
(r::J 5)
(p
V
(p e q)
I ... p
I ... q
I ... (P::J r)
(p v q)
(p v q)
-p
-q
I ... q
I ...
D N.
p :: --p
~
(p e q)
A.d.Q..
p
q
I... (p v q)
I... (p v q)
P
Comm.
(p v q) :: (q
v
(p
e
e
q) :: (q
A5S0C.
p)
p)
((p v q) v r) :: (p v (q v r)
((p e q) e r) ': (p e (q e r)
r)
I .., (q v 5)
D..!.!..IL
De M.
BE.
p : (p v p)
-(p v q) :: (-p e -q)
-(peq):: (-pv-q)
(p=q) :: ((p::Jq) e (q::J p))
Contrap,
G.£
(p::J q) :: (-q::J -p)
(p::J q) :: (-p v q)
Exp,
((p e q)::J r) :: (p::J (q::J r))
CP,
Dist.
(pe(qvI')):: ((peq)v(per))
. (p V (q e r)) :: ((p v q) e (p v I'))
[P
q
Q.lL
-(x)¢x :. (3x)-¢x
-(3x)¢x :. (x)·_¢x
- (x) -¢x :: (3x)¢x
- (Jx) -¢x :: (x)¢x
I ... -p
I ... (p::Jq)
C.Q.N
ill
ti
-(x) (¢x ::J \Vx) :: (3x) (¢x e -\Vx)
-(::Jx)(¢x e \Vx) :: (x)(¢X::J -\VX)
-(x)(¢X::J -\Vx) :: (3x)(¢x e \VX)
-(Jx)(¢x e -~/X) :: (x)(¢x::J \Vx)
(x)¢x
(3x)¢x
provided
we flag a
I ... ¢a
I ... ¢a
U,G,
flag a
I ' (3x)¢x
[
¢a
I ... (x)¢x