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In page Binary relation:

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If relations over proper classes are allowed:

  • Set-like (or local): for all x in X, the class of all y in Y such that yRx, i.e. { y ∈ Y : y R x } {\displaystyle \{y\in Y:yRx\}} , is a set. For example, the relation ∈ {\displaystyle \in } is set-like, and every relation on two sets is set-like.[7] The usual ordering < over the class of ordinal numbers is a set-like relation, while its inverse > is not.[citation needed]