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

SECTION C]

SIMILARITY OF CLASSES

481

The class of domains is D"/3, and we have (P). E! DP. Hence we have
only to prove (putting D in place of the R of *73-25)
P, Q e3. D'P = D'&Q. )p, Q. P = Q,
which, in the case supposed, is proved immediately.
*73-26. ~: y ~,1:~.RPs RC)s
Dem.
I. *33-431.: )FHp. ). R 1-+ 1. /C (PcR.
[*73-22] R. R"13 sm.. R r 8 e (R"/3) Rin DI:)F.Prop
*k73-27..Ry=Rz._,.~=z:I " mP~RrPe(CP n
[*73-26. *71-57]
*73-28. F:: y,zc,8.Dy,,:RCIy=Rcz.-..y=z:. D
R"/3sm/3. R r 3e (R"/3) iTh/
Dem.
F. *71-58.*73 03.*37-421.)I-: Hp.). R r /3e(R"/3) 9T3: )F.Prop
*73-3. F. a sm a. Ia a smKIa
Dem.
F. *~50-31. *24 -~11. F - a C (11 (I
F. (1). *A72-17 - *i50-16. F. l I - - + 1. a C (I'll. l~a = a (2)
F.(2). *73K142-04. )I. Prop
This is the reflexive property of similarity. The conditions of significance
require that a should be a class of some type, but impose no restriction as to
the type of class.
*73-301. F:Rca m-,8.s-s.Re,89 —a
Dem.
F. *73-03. *71212. *33-2-21.
I- B E aI STh /. B e 1 f -)1. D'Bi = P3. (PB = at.
[*73-03].Re Tm ha: DF. Prop
*73-31. I- asm /. =. /sma [*73-301-04. *31-52]
This proposition shows that similarity is a symmetrical relation.
*73-311. F:Rea ct h/. Se/3 y.).R1Sea thsmy
Dem.
F. *73-03. *71-2052. )F: Hp. R. RISeI-*1 (1)
F.*73-03.*37-32. )F:Hp.).D'( IS)=IR"/3.EII'(B RS)=S"/3.
a = D'R.3 =EI?. / = D'S. c Py G"S.
[*371~25)] Dc D(R I S) Gc I I(R I S) = y (2).(1). (2). *73-03. ) F. Prop
R. & W. 31