defined the ordered pair so that its projections could be proper classes as well as sets. (The Kuratowski definition does not allow this.) He first defined ordered pairs whose projections are sets in Kuratowski's manner. He then redefined the pair

where the component Cartesian products are Kuratowski pairs of sets and where

This renders possible pairs whose projections are proper classes. The Quine-Rosser definition above also admits proper classes as projections. Similarly the triple is

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