Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

126

126 ~~~~MATHEMATICAL LOGIC[PRI

[PART I

*4-6.
*4-61.

F:
F:

p )q.-. -~pvq
r- (p ) q). =E -p. - q

l*-4 -6 2. F: p:),,q. =. pv q

*4-63.
*4-64.
*4-65.
*4-66.
*467.
*4-7.
Demr

F: -p:)-q).n-.p.q
F: -p:)q.u=.pvq
F: rpq.n~..
F: C,.p Drdq. n.p v - q
F:.p:)q.:p.:).p.q?l..) q
P

[*4-2. (*1-01)]
[*4&611-52]
*4.6 -..q]
[*4-62411 5]
[*2-53-54]
L*4-6411.56]
*4-64 <1q
[*4-66-11-54]

F. *.327.Syll.) F:.p. D. p. q:). p )q

(1)

F. Comp
[Exp]
[1d]
F. (1).(2).

) F:.pD I)p. p q.:P. ).p q:.
) F::p )p.D):.p )q.::P. D.P..:
D F:.p D q. )::P D. P. q
D F. Prop

(2)

Dern.
F. *321.:P...:). -P q
[*3-26]:) F:.p. ). P. q: ):p - - P.q
F. *326. DF..-.P:D.D-
F. (3). *4-722. ) F.Prop

(1)
(2)
(3)

The above proposition is constantly used. It enables us to transform
every implication into an equivalence, which is an advantage if we wish to
assimilate symbolic logic as far as possible to ordinary algebra. But when
symbolic logic is regarded as an instrument of proof, we need implications,
and it is usually inconvenient to substitute equivalences. Similar remarks
apply to the following proposition.
*4-72. F:.p~q.rr:q.u-.pvq
Dem.

PI qj
[*4412]
[*4'S57]
[*4'31]

=q. =.pvq:. ) F. Prop