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

SECTION D]

M SCELLANEOUS PROPOSITIONS

551

*85-44. F: c e Cls2 excl. ). ea's't sm ee4 C
The following propositions depend upon the definition
*85-5. P I y = y"P'y Df
I.e. P I y is the class of all couples whose relatum is y while the referent
has the relation P to y. We then have
*85 53. F. Pa'a = "D"e^'P I "a
giving a construction for IP'a by means of e4, and
*85-54. F. P' snm e'P "a
which reduces the question of the existence of P-selections to that of
the existence of e-selections.
*85'61. F. e I"/ e Cls2 excl. eCa' = s"'D"e^a' e I. e&'K sm e'4e K
This proposition gives a construction for any c-selection in terms of an
e-selection from a Cls2 excl, and reduces the question of the existence of the
former to that of the existence of the latter. A particularly important case
is when K= Cl ex'a. This is considered in
*85-63. F: e "'Cl ex'ae Cls ex2 excl! ea'Cl ea. ex 'e i"Cl ex'a
*851. F: Q r X e Cls - 1.. D"Qa'X = D"ej'Q" X
Derm.
h. 81:3. D: Hp. 2. ])"Q,' =,u {a e Q". 2,. n a e 1: t c s'Q"X} (1)
F. 84-51. h: Hp. ). Q"x e Cls0 excl.
[*84-412] D. D"E,'Q"X = {a eQX. ),.. n a e 1: I C s'Q"X} (2)
F.(1). (2).. F Prop
*85-11. F: Q e 1 - 1. D. D"(P Q)I'= D"P
Dem.
F. *33-431. *32-12. D: Hp.. X C C' (1)
F. (1). 82-32. D F: Hp.. D"(P Q)'x = D"P'Q"X: D F. Prop
*85-111. F: M e eA'Q"X. D. D'(M Q. x) = D'M [*82-3]
*85'112. F: Me e'Q"X...M Q Q'\ L82 221 p2
*85-12. F: Q r X e -- 1.. D "Q,' = D"ea'Q" X
Denm.
F. *62'26. F. D"Q,'x = D"(e Q)A'x (1)
F. *8232. F: Hp. D. D"(e I Q),'X = D"e'Q" (2)
F. (1). (2). D F. Prop
This proposition is used in connection with ordinal multiplication (*173'14).