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

122

MATHEMATICAL LOGIC

[PART I

*44. F:.p. qvr.-: p. q.v. p.r*441. f:.p.v.q?r:=.pvq.pvr
Thie second of these forms has no analogue in ordinary algelra.
*4-~71.: g. i p
I.e. p -implies q when, and only when, p is equivalent to p. q. This
proposition is used constantly; it enables us to replace any implication by
an equivalence.
*4-~73. F..)p=.~
I.e. a true factor may be dropped from or added to a proposition without
altering the truth-value of the proposition.
*4-01. p=-q.=.p)q.q)p Df
*402. prqrr.=.prq.qnr Df
This definition serves merely to provide a convenient abbreviation.
*4-1. F:p q.D.cNq -p [*2-16-17]
*4'11. F p q p q [*3'201 617. *3-47'22]
-412. F: p q.. q p [*2-03-15]
*413. F. p-(, (p) [*2-12-14]
-*4-14. F:.p - q D. r::p r [*3-q Cc337 *4kS13]3
*4-~15. F.pq 7. ' [322 *49~13-14
*4-2. F.prrp [Id. *3-2]
*421. F: p q.q p [*3-22]
*422. F: p q. q nr.pnr
Dem..*:3-26 ) F:p q. qr q
[*3-26] ).pq (1)
F. *327 ) p q.q r q
[*3-26] q r (2)
F-.(I). (2). *2~83 D t p q. q r. P D r (3)
F. *3-27. F q. q r.. q=nr.
[*3:27] ).r q (4)
F. *3'26. DF:p nq q r ~p = q
[*:327] ).q (5)
F.(4). (6). C 3 F. p rop (6)
F.(3).(6). Comp. D F. Prop