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{a, b} = c and a = c implies that c is an element of c, contradicting regularity.
:So we have a = c and {a, b} = {c, d}, and so: {b} = {a, b} \ {a} = {c, d} \ {c} = {d}, so b = d.

Quine-Rosser definition

Rosser (1953) employed a definition of the ordered pair due to Quine which requires a prior definition of the natural numbers. Let be the set of natural numbers and define first

The

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