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

386

386 ~~PROLEGOMENA TO CARDINAL ARITHMETIC [ATI

[PART II

*554161. F-x y t'IR (D'R = tw.PGR = t'y)
Dern.
F. *55-16. *20-15.)
F..R(D'R = t'x.G'R= t'y) = R(R = x41)
[*51-11] = ff(x 1y) (1)
F()*51P51. ) F. Prop
*55-17. F xj4y =t (Dt~ U't'Yy) [*55-161. *33-6611
*55-2. F: X y= X IZ.=-.,y= Z
Dem.
F. *30-37. *55-11-12. ) F:yz.:). x Iy =:xz (1)
F.*30,37. *33-121.
F: x~y=xz I Z. G'x y=(x ~I'Z.
[*55-15] C.ty - Vz.
[*51-23] Y = Z (2)
F. (1). (2).:) F. Prop
*55-201. F:xlz=ylz.=E.X=y
*55-202. F:xjy=zjw.-.x=Z.Y=W.E=.yjX=wjz
Dern.
F.*55-2201.)
[*13.17] )x Y Zw W~
F.*30-37. *33-12-121.)3
F:x 4y=z 4w. D. DIX 4 y = D'z 4w. (cl'x 4y =(1'z 4w.
[*55-15]:). t = t'z. =" - t'W.
[*51V23] x = z.,y= W (2)
F.x yz1wE.x(2y) (3
Similarly
F: Y IX= WI Z..=Z. Y= W (4)
F. (3). (4).:) F. Prop
The above proposition is important.
*55-21. F. G1x 4 V. U,' 4 xw= V [*33A432. *55-12-121]
*55-22. F.D'x4=R[(Hjy).R=xrjy} [*55-122]
*55-221. F. D' 4x= B (gy). R= y 4,x [*55-123]