Chapter 7
PD Rules

PD includes all of the old SD rules. So, go ahead and use MP or RD, etc. as needed.

The first rules new rules:
^E
input:

output:
(^x)P

 P(a)
%I
input:

output:
 P(a)

 (%x)Px
QN
(Quantifier Negation)
~(^x)P (%x)~P
or
~(%x)P (^x)~P

 

In 7.3 we define:

^I
input:

output:
P(a)

(^x)P

Provided 'a' is arbitrary in this sense:

  •  'a' does not occur in any premise or in the assumption of a subderivation still in progress (unterminated).
  •  'a' does not occur in P.