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

SECTION B]

DESCRIP'IriONS

18'7

SECIO B] DES (qCR:IPTIONSx18b):7OX.. X.=b:b=c:.
[*14-11T =:. (He) *X - =-2~ X =C: (7x) (OX)= C:
[*14413] ( e) *x s =- x x = c = (x) (x):
[*14-1]. (ix) (rx) = (ix) (ox):) I-. Prop
In the above proposition, in accordance with our convention, the descriptive expression (ix) (ox) is eliminated before (ix) (fx), because it occurs
first in " (ix) (ox) = (ix) (xrx) "; but in "(ix) (*x) = (7x) (fx)," (ix) (#x) is to
be first eliminated. The order of elimination makes no difference to the
truth-value, as was proved in *14-113.
The above proposition may also be proved as follows:
F. *14-1 11.) F ('ix) (ox) = ('ix) (*fx).
= (b, c): Ox. =,.x=b: *x. -. x=c: b=c:
[*4-~3.*c13-16.*11 111r341] =:(Hb, c): *x.=x, x= c: ox.=x,.x=b c=b:
[*11-2.*14-111] - (i (x) (#x) = (7x) (ox) ). F. Prop
*14-14. F a = b. b = ('ix) (x).. a = (ix)(Ox) [*13-13]
*14142. F a = (ix) (ox). (7x) (ox) = (ix) (#x). ). a= (x) (#x)
Dernt.
F. *1 4-1. ) F Hp. ):. (b): Ox.=-x x = b a= b:.
(ajc) fOx. =. = c c ==(7x)(#x):.
[*1-31195] Ox. x = a:. (atc) Ox =~ x = c: c = (ix) (*x)
[*10:35-] ( e) Ox x x = a Ox = x x = c: c = (,ix) (*x:
[*14-121] ):.(ac) O./x. =.x==a:a=c: c=(ix)(#x):.x
[*3-27.*13-195] ):. a = (ix) (#x):: ) F. Prop
*144144. F (ix) (ox) = (ix) (ifrx). (ix) (#x) = (ix) (Xx).) (ix) (x)= (7x) (Xx)
Dern.
*1 4-1 111 D F:: Hp D. (Ha, b): Ox-x. x = a *a. =X. X = b: a = b
(jEC, d):*x. =. x = c xx. x. x= d: c d:.
[*~13-195] ~.. (sa) Ox.,=. x =a: cxx. =. x =Ca:.
('x. X. X = C xx. =.T. X = C:.
[*k14-121.*k11-42]. (Ha, c): Ox =rx. x= a: XxC. =-x. x cC: a c:.
[*14-111] )(ix) (ox) = ('ix ((x)::)D F. Prop
*14-145. F:a =(ix) (oJx). a = (ix) (#x). ). (7x) (ox) = (ix) (*fx)
Dem.
F.*141..: a = (u) (ox). (ab) Ox. x = b: a b
[*13-195] Ox- x.x