EDB β€” 239

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E195

[239]Prerequisites:[01R],[(3.171)],[24V].Let x,y be elements (generic, not necessarily natural numbers), such that

(1)xβŠ†yβŠ†S(x)
196

prove that

x=y∨y=S(x);

where the above two are mutually exclusive, and (in the hypothesis ?? above) the second one holds if and only if x∈y; summarizing

1β‡’(x=y⟺yβ‰ S(x)⟺xβˆ‰y).

Note the analogy with [22H].

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