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

SE~CTION D] LIMITED DOMAINS AND CONVERSE DOMAINS28

281

Dern.
l-.*23-33.)F:x{(alR)A(/31S)1y.a -~.x(alBR)y.x(/31S)y.
[*3051] -=S xceea. xRy. x e/. xSy.
[*22-33.*23-33] 7-7.WEc(a ri/3).x (RA S) y.
[*3.51] ~. x Ra AI)j1(R AS)}y: ) F. Piop
*35-14. F.(B ra) A (S ri) =(R AS)r~(anA /) [Similar proof to *35-13]
Dem.
F. *35-11)
[*35-13-14] = {(a n a') 1BA S)} A {(-R A 5) fr (/3 A,'
*35-16. F.(aljR)AS=al(RAS)=BRAa1S [Similar proof to *30513]
*35-17. F.(Rr )AS=(RAS~rj3=BASr/3 [Similar proof to *35-13]
*35-18. F.(a1R3,)AS=a1l(RAS4/38=BAalSr/3
[Simnilar proof to *35-15]
*35-21. F.ajBr/3=(ajR)r,/3=aj(Rr/3)
Dent.
F*35-102.)F:x (a1Br,8) y..x a. xRy. y c3.
[*35101] * ~~~~~x {(a 1 B) r /81 y'(1
F. *35-102. )F::x(a1B r3) y.~.x a. xRy. y c/S.
[*35-101] zE xea. x(R r/8) y.
F(1).(2). ) F. Prop
*35'22. F.(ajR)iS=aj(RjS)
Dem.
[*35-1]:(Hjz).wxe a. xRz. zSy:
[*10-35] Ex ea: (qz). xRz -Zsy.
[*34-1] -:xca.x(RIS)y:
[*35-1] =:X la 1(B IS)ly:. DF. Prop
*35-23. F. S I(B R3 (S B ) r /3 [Similar proof to *35-22]
*35-24. a1RjS=(ajR)jS Df
*35-25. S Rr/3=(SIR4/3 Df