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

360 PROLEGOMENA TO CARDINAL ARITHMETIC [PA RT Ii
Dent.
[*10-22]:.Z = X. Dz. Oz: z E/3 ). c, z:.
[*13.191] E-:wO:zE/3.),.cfz::.)F. Prop
*51-239. F::a-t'xu/3. ):.(a1z).zea.oz.=:c/x.v.(az).zeI3.4z
Dem.
F. *51-237.)D
F:: Hp. ):. (az). za. z.= (az):z= x *v *z E/3: z:
[*4-4] (HQZ):z = X. OZ. v. zE/3.OZ
[*10-42]:(Hz). z= X.qOZ.V. (3z). z 6l. Oz:
[*13-195] O~x. v.(gz). z e/3. z::)DF. Prop
*51-24. F:.t'yCt'xuI3.E:y=x.v.yefl
Dem.
F.*51-236.)D
F:: t'Y C t'Xv/38.:zect',y. ),:z =wX. V..ze/3:.
[*51-15] ~ Z= Y. ),: z= X. V. z f:.
[*13-191]:y =x. v. yf:: ) F.Prop
*51-25. F:aCt'xu/3.xr.ea.).aCfl [*51-211.*24-49]
*51-3. F:yea.y~x..yea-t'x [*51-15. *22-33-35]
*51-31. F:!a A t'x. t~.L'x C a.* a A -lv t'x. Xe a
Dent.
F *22-33. *51-15. a:!a t'x..(jy)..y a. y x.
[*13-195] X- Xa. (1)
[*51-2] ~ t'X C a. (2)
[*22-621] z (x = t'x Aa (3)
F.-(1).(2). (3). ) F. Prop
*51-34. F: x ea.-.-a C -t'x [*51-2. *22-81]
*51-35. F:x~ea.=n.t'xC-a [*51P2.*22-35]
*51-36. F:xe-ea. —.aC-t'x [*51-35.*22-811]
*51P36 is frequently used.
*51-37. F. a = '('xCa) [*51-2. *20-33]