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

SECTION C] ASSOCIATIVE LAW OF RELATIONAL MULTIPLICATION 45

455

*174-361. F-: P ERel arithm. ).CG'P CRe 1 excl
Dem.
F.*162-1.F:Qe C'P. ).Q C VP (1)
F.*174-3.)F:Hp.:).V~PcRe12 excl (2)
F.-(1).(2). *163-43. DF.Prop
*174-362. F- P E Re 1 arithm. Q, Q' e G'P. C'P"'Q = C"'Q' TV Q,
Dem.
F.*174-322. D F:Hp.! C,"C'Q. D. Q =Q' (1)
F.*37-45. )F: C"G'IQ =A.).'Q=A.
[*33-241].Q = (2)
F.-(2). *13-172. FHp.GW'ICQ =A.D. Q =Q' (3)
F.(I).-(3) ) F. Prop
*174-363. F: P e Re 1 arithm.) Prod; P E ReP1 exci
Dern.
F. *173-161. *174-361. *173-2. Transp.:)
F:. Hp.) D: Q, Q'eG'"P. a!C'Prod'Q r C'Prod'Q'. D.
a! Prod'C"6C'Q nProd'C"C'Q'.
[*110523.*1 74-33] ).C"C'Q = G"G'Q'.
[*174-362] ) Q= Q.
[*30-37] ).Prod'"Q Prod'Q' (1)
F.- (1).- *1 63 11. *1 50'2 2.:) F. Prop
*174-4. F: Pe Re12excl.P CJ.:).
Prod'IX'P = D; h Prod '1Vl P 8; De; Prod'n1; P
Dem.
F. *173-1. F F. Prod'V'P-=D; '1' (1)c
F. (1). *174-24. F F: PE Re12 excl. P CJ. ).Prod'I'P-=D;;Prod'Wl;P
[*41 -43] = s;D,; Prod'L1 P: ) F. Prop
*174-401. F: PeRel~arithm. ). Prod'Prod;P=D,;Prod'flVP
Dem.
F.*80-33.*162-23.:)F:RecF4'G'Q.:).D'1RCCG'~'Q (1)
F (1). ) F: R eF4'C'Q.- R'cFi('O'Q'.a D'(Rri D'R'.)
Q = Q'.[*81-21.*174-361.*163i12] D. B = I' (3)
F. (3). *33-241. )
F:. Hp.)D: Q, Q'EG"P. Re F4'GQ. R'e F4'G'Q'. D'R D'R'. R.1 1':
[*1 72-12.*150-22]) D s'G"Ilfl'%JP e 1 -+ 1:
[*162-22] ):D C% G';PE l — * 1:
[*173-33] D D,;Prod'JflP =Prod'D t1V;P
[*173-1] = Prod'6Prod;P:. D F. Prop