 In his survey of PM, Quine (1951: 155) complains that this last 100 pages of Part I is occupied with proving theorems relating redundant definitions of the same notions. Thus PM defines the notion of domain and range and then introduces notions that again define the same classes, which are proved to be equivalent. PM defines the notation  of ‘\(R\pmdq\beta\)’ to be read as “the terms which have the relation R to members of \(\beta\)” and uses the example: