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Definition df-fin4 9053
Description: A set is IV-finite (Dedekind finite) iff it has no equinumerous proper subset. Definition IV of [Levy58] p. 3. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin4 FinIV = {𝑥 ∣ ¬ ∃𝑦(𝑦𝑥𝑦𝑥)}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-fin4
StepHypRef Expression
1 cfin4 9046 . 2 class FinIV
2 vy . . . . . . . 8 setvar 𝑦
32cv 1479 . . . . . . 7 class 𝑦
4 vx . . . . . . . 8 setvar 𝑥
54cv 1479 . . . . . . 7 class 𝑥
63, 5wpss 3556 . . . . . 6 wff 𝑦𝑥
7 cen 7896 . . . . . . 7 class
83, 5, 7wbr 4613 . . . . . 6 wff 𝑦𝑥
96, 8wa 384 . . . . 5 wff (𝑦𝑥𝑦𝑥)
109, 2wex 1701 . . . 4 wff 𝑦(𝑦𝑥𝑦𝑥)
1110wn 3 . . 3 wff ¬ ∃𝑦(𝑦𝑥𝑦𝑥)
1211, 4cab 2607 . 2 class {𝑥 ∣ ¬ ∃𝑦(𝑦𝑥𝑦𝑥)}
131, 12wceq 1480 1 wff FinIV = {𝑥 ∣ ¬ ∃𝑦(𝑦𝑥𝑦𝑥)}
Colors of variables: wff setvar class
This definition is referenced by:  isfin4  9063
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