Rules of Inference
&E
input:

output:
P&Q

P
or P&Q

Q
&I
input 1:
input 2:

output:
P
Q


P&Q
DS
(Disjunctive Syllogism)
input 1:
input 2:

output:
PvQ
~P

Q
or PvQ
~Q

P
MT
(Modus
Tolens )
input 1:
input 2:

output:
P>Q
~Q

~P
MP
input 1:
input 2:

output:
P>Q
P

Q