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

524 SERIES [PART V
I t ~~- 4 -*200-54. F: P Cf.!! P.).p'P"'P p'PI~a} =p'P"p'PCa
Dem.
4- 4
F. *40O62. ) F: a! a. D. C'P rip'PCC =p Pgpca (1)
4 -F.*40-2. DF:a=A.D.p'P1x=a=V. (2)
[*40-16] ).pCP(C p'P"a C p'P"C'P (3)
-t -
F. (3). *200-51. ):Hp. a = A. ).p'Pcp'P CC a=A (4)
4 -F.(2).*24<26. F:o==A. ).C'Pnp'P" a=G'P (5)
-4 4tF.(5).*200O51. )F:Hp.a=A. ).p'Pc"(C'P p,'Pla)= A (6)
F.(1).(4). (6).:)F.Prop
This proposition is a lemma whose purpose is to avoid the necessity of
introducing the hypothesis q! a in proofs in which it is not really necessary.
The first use of this proposition occurs in *206551.