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

SECTION A]

SECTION A] CARDINAL COUPLES:7

379

Dem.
F.*54'4.:)F::a=t'wvffy.:):.
/3 C a. - H! 3. /38= A. v.8 /= t'x.- v. /3 =.' v., /3aC: H! /:
[*24053-56.*51-1(1] /38 = t'~x. v. / =." v V. / = a (1)
F. *54-25. Transp. *52-22. ) F: x =+ y.)D. t'x v i/y 4 t'x. it'x v t'y t~= ly:
[*13-12] D F: a-=t'xv t'y. x +Y. D..a jfx. a +t'y (2)
/3 C a.! /3., /3. 4 a* 3 = ffx. v. 3 - ly
[*51-235] (HZ). z 6 a., /= ffz:
F. (3). *111.1835. *54'101. D F. Prop
*54-43.:,/ 1.: /3A.a32
Dern.
F. *54-26.) F:. a=tfx. /3= t'y. ): a /E 2. -. x+y.
[*51'231] *- ~( A nc =A.
[*13-12] Ea/= 1
F.(1).-*11-11'35.)3
F:. (ax, Y). Ot= ~'x./3=1y. D: a v/32. -arl3= A (2)
F. (2).-*1 154. *52-1.)DF. Prop
From this proposition it will follow, when arithmetical addition has been
defined, that 1 ~ 1 = 2.
Demn.
F.*51-234. *1 162.)F:.zwe' Wtx v ~'y. W (z, w).
Z e VI t'y.:)Z. f (Z, x). 0 (z, y)
[*51-234.*1O-29]:4(x,x). c (x, y). 0./(y, x). 0 (y, y):. ) F. Prop
Dern.
F. *5-6. ) F:: z, WE lvt. z+W. )Z (z, w):z, WE lv t'y. Dz:= w v. 4 (z, w):.
[*54-44] E:w=x.v.O(x~x):x=y.V.cp(x'Y):
[*I -16*4-1] =: =.. 0(xy) 0 y = x) *v.~(,x y )
This proposition is used in *163-42, in the theory of relations of mutually
exclusive relations.