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

SECTION D] THE RELATIVE PRODUCT OF TWO RELATIONS25

275

*3451. FX13y. (HZ, W). X11Z. ZRW. WRy
Dent.
F*34-1.(*34-03).):XR3,y *Hw).x.R2W.WRy:
[*34-5] (aqw): (~jz). xRz.z-Rw:w-Ry:
[*1 1155] (sw, z).xRz. z-Rw. wRy:
[*11I 2]:(HjZ, I) R. xRz w. wRy:. DF. Prop
*34-52. F. R3= 11112 *321]
*34-53. F t4! 112 - Dc- (I'1 [*34-3]
*34-531. F D'11 rnWPR =A.=. R2= A [*34053. Transp]
*34-54. F:XRX.). XR2X
Dent.
F *4-24. ) F: xRx. D. xRx. xRx.
[*10-24]:). (ajy). x-Ry. y-Rx.
[*34-5] ).xR2X:DF. Prop
*34-55. F. 12CS xRy- yftz.:)~~. XSZ [*34-5.*10-23]
*34-56. F. D'112 C D'11. (1IR2 C (1'11. GC112 C CJ'R [*34-36-38]
*34-6. F.RS _R2 tAS2
Dent.
F.*345.):X (_R tjS)2y *(HZ). X(R tAS) Z. Z(R AS) y:
[*23-33.*10-281] (az). xRz. xSz. z11Y. zSY:
[*4-3.*10-281] (az). xftz. zRY. XSz. zSY:
[*10-5] D) (HZ).XRZ.ZSy:(qz). xSz.zSY
[*34-5] ):XR~y XS2Y
[*23-33] D:x(R2AS~ 2) y(1
F. (1). *ii'ii.F. Prop
*34-62. F(1S)= 12wRS viSRS
Dent.
F.*34-26. )F.(1 )2=.R (R tu S) wu S I(11 v 5)
[*34k25] R12 viR vS I.S -R US2.) F. Prop
The above proposition is a lemma for *160-51, as is also *34-73, which,employs the above proposition.
*34,63. F. Criv'(112) (CnvcR1)2
Dent.
F. *31-131.)D
F:. xfCnv,'(12)},y yR2x:
[*34-5] E(az). y~z. ztx:
[*31K131.*10-281] E(az). x-Rz. zRy:
[*31-131.*34-5] x (Cnv'11)2 y::) F. Prop
18-2