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

118

MATHEMATICAL LOGIC

[PART I

*3-33. F:p~q.q r.2'.p~r [Syll.Jmp]
*3-34. F:q~r-p~q.).p~r [Syll.Irnp]
These two propositions will hereafter be referred to as "Syll"; they are
usually more convenient than either *205 or *2-06.
*3-35. F:p.p gq.D>q [*2-27.Jmp]
*3-37.:pq:r: p-rD,
Dem.
F. Transp.D F:q )r.). r)?~D q:
[SY11] DF:. p.D- q r:D:P.D. CUr Dhi (1)
F. Exp. F:.p q.).r:):p.).q r (2)
~.Imp. D ~:.p. D., D —,: p., r. D.q (3)
F(2). (l). (3). Syll. ) F. Prop
This is another form of transposition.
*3-4. F:P p. q. ). p q [*2-51. Transp. (*101. *3-01)]
*3-41. F:.pDr.):p.qD.)r [*3'26.Syll]
*3-42. F:. q~r.D: p. q D-i [*3~27. Syll]
*3-343. F:- p D q ~ - p D r. D:. D.
Dem.
F.a*3-2.D:.q.D: r..q.D r (1)
F.- (1).- Syll.) F:: p D q. ):. p.) D..q.r:
[*2'77] D:.pDr.:p..q.r (2)
F.(2). Imp. DF. Prop
*3-44. F:.q:)p.rrp.):qvr.).p
This principLe is analogous to *3-43. The analogy between *3-43 and
*3-44 is of a sort which generally subsists between formulae concerning
products and formulae concerning sums.
Dem.
F. Syll. D F:. q D r* r )p.): q )p:
[*26] D:qDP.).p (1)
F. (1. Exp. D F:: q )r. ):. r p.: q )p. D p:.
[Comm.lmp] D:. qp.rlp.)Dp (2)
F.(2). Comm. ) F:. q )p. r )p.): q ) r. ).p:.
[*2-53.Syll] ) F. Prop