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

262

262 ~~~~MATHEMATICAL LOGIC[PRI

[PART I

*33-13. F:xeD'B.=E.(3y).xRy
*33-131. F y e G'R. ~(ax) xRy
*33 132. F:.x eC'R. (3y):xRy.v -yRx
*33-14. F xliy D.)xceD'RyE G'R
*33-16. F.G'B= D'R vGBR
*33-221-22. The converse domain of a relation is the domain of its converse,
the domain of a relation is the converse domain of its converse, and the field
of a relation is the field of its converse.
*33-4. F.D'R-= ^ l3'R'(x}
with corresponding propositions (*33-41-42) for (IUR and C'R.
*33-43. F:E!R'y.D.yeEVB-f.R'yeD'R
*33-431. F:(,y).E!R'y.:).(13).1t3CG'B
*33-5. F-CG= F
*33-51. F xsG'B.E.xFI
The proofs of propositions concerning (I and C are usually similar to those
for D, and are therefore often omitted.

*33 01. D = &B-R [a = X {(3y). x~yJI]

Df

*33-02. (I = 18R [1 1 (2x). xwRy] Df
*33-03. C = -^y'R'[,y= {(3y): xRy. v.yRxl] Df
*3304. F xR {(2[y): xRy. v. yRx} Df
*33-1. F: aD]?. * a = ~ (Hy).xRy} [*2139. (*33-01)]
*33-101. F: 13011?. -.138 = 9 {(gx). xRy}
*33-102. F: yCR.=.,y=5{f(gy):xRy.v.y-RxI
*33-103. F:. xFR. -: (ay): x]Ry.v. yRx
*33-11. F. D'JR = ^ f~(ay). xRy} [*33-1. *30-3. *20-59]
*33-111. F.0(I']? = 9 {(ax). xRy}
*33-112. F. C']? = X^ t(au): xwRy. v. yRx}
*33-121. F. E! CUT
*33-122. F. E! C'R
*33-123. F: aDR. =* a = D'R [*30-4. *33-12]
*33-124. F: 318fR..1=01']=?[ I [*30-4. *33-121]