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Full Idea
A 'proper class' cannot be a member of anything, neither of a set nor of another proper class.
Gist of Idea
A 'proper class' cannot be a member of anything
Source
David Bostock (Philosophy of Mathematics [2009], 5.4)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.151