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

SECTION D] CONDITIONS FOR THE EXISTENCE OF SELECTIONS56

567

*88-41. F.Cl"K C6Cls2 M4ult [*88'42]
*88-411. F.K ED"E4',eCI"(K
F. *35-52. DF CK1C)=G(lK
[*35-65.*33,431] = K(1
F. (1). *884. ) F. (a-R). R E ea'Cl "K.D'R = K.
[*37-6] D F. Ke D D",e'Cl "Ic ) DF. Prop
*88-42. F:KEClIS2 Mult.g~a.- KCV t'aE Cls2 MUlt [*83-904.*(88-2]
In virtue of this proposition, as will be proved later, every finite class
of existent classes is a Cls2 Mulit. For we have A c e4'A; and, by the above,
a Cls2 Mult remains a Cls2 Mult when one existent class is added as an
additional member; hence the result follows by induction.
*88-43. F 8 SCK e 0Is-2 MUlt. ).ed411K E Cls2 Mul~t
Dem,.
F. *882. ) F Hp. D. a! E4'sSlK.
[*85-24] D).a! ~"D"E4C'E46, C K
[*88-2] D. E4j"'K E Cls2 Mut t: D F. Prop
*88-431. F:. K E l2excl. D6E4"K E 62Mut S'K E 2Ml
[*88-2. *85-28. *37-45]
*88-44. F: Cl ex's'K cE Cls2 Mullt. D). K - t'AE Cls2 MUlt [*60-57 *88&22]
*88-441. F: A1JE K. Cl ex's'K E ClS2 MUlt..DK E ClS2 MUlt [*88&44]
*88-45. F:D'.R 'R = A.P = S,&{ xe6 'R a = R'X Vt'X}.)D. P 6ee'(IJ'P
Demn.
[*51-16]:)x" x ea (2)
F.Hp.)D: xPa. D,. ac= R'w u t'x. R'x C D'R.- t'x C EJ1'R.
[*24-494]:)X. a- D'R = tx(3)
[*20-23.*5V 123]:)X1 I X= =
[*71-17]:P 6Il-+ CIS (4)
F. (2). (4). *80-14. DF.Prop