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Definition df-fin2 8964
Description: A set is II-finite (Tarski finite) iff every nonempty chain of subsets contains a maximum element. Definition II of [Levy58] p. 2. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin2 FinII = {𝑥 ∣ ∀𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-fin2
StepHypRef Expression
1 cfin2 8957 . 2 class FinII
2 vy . . . . . . . 8 setvar 𝑦
32cv 1473 . . . . . . 7 class 𝑦
4 c0 3869 . . . . . . 7 class
53, 4wne 2775 . . . . . 6 wff 𝑦 ≠ ∅
6 crpss 6807 . . . . . . 7 class []
73, 6wor 4944 . . . . . 6 wff [] Or 𝑦
85, 7wa 382 . . . . 5 wff (𝑦 ≠ ∅ ∧ [] Or 𝑦)
93cuni 4362 . . . . . 6 class 𝑦
109, 3wcel 1975 . . . . 5 wff 𝑦𝑦
118, 10wi 4 . . . 4 wff ((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)
12 vx . . . . . . 7 setvar 𝑥
1312cv 1473 . . . . . 6 class 𝑥
1413cpw 4103 . . . . 5 class 𝒫 𝑥
1514cpw 4103 . . . 4 class 𝒫 𝒫 𝑥
1611, 2, 15wral 2891 . . 3 wff 𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)
1716, 12cab 2591 . 2 class {𝑥 ∣ ∀𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)}
181, 17wceq 1474 1 wff FinII = {𝑥 ∣ ∀𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)}
Colors of variables: wff setvar class
This definition is referenced by:  isfin2  8972
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