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Definition df-fin2 9314
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 9307 . 2 class FinII
2 vy . . . . . . . 8 setvar 𝑦
32cv 1630 . . . . . . 7 class 𝑦
4 c0 4063 . . . . . . 7 class
53, 4wne 2943 . . . . . 6 wff 𝑦 ≠ ∅
6 crpss 7087 . . . . . . 7 class []
73, 6wor 5170 . . . . . 6 wff [] Or 𝑦
85, 7wa 382 . . . . 5 wff (𝑦 ≠ ∅ ∧ [] Or 𝑦)
93cuni 4575 . . . . . 6 class 𝑦
109, 3wcel 2145 . . . . 5 wff 𝑦𝑦
118, 10wi 4 . . . 4 wff ((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)
12 vx . . . . . . 7 setvar 𝑥
1312cv 1630 . . . . . 6 class 𝑥
1413cpw 4298 . . . . 5 class 𝒫 𝑥
1514cpw 4298 . . . 4 class 𝒫 𝒫 𝑥
1611, 2, 15wral 3061 . . 3 wff 𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)
1716, 12cab 2757 . 2 class {𝑥 ∣ ∀𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)}
181, 17wceq 1631 1 wff FinII = {𝑥 ∣ ∀𝑦 ∈ 𝒫 𝒫 𝑥((𝑦 ≠ ∅ ∧ [] Or 𝑦) → 𝑦𝑦)}
Colors of variables: wff setvar class
This definition is referenced by:  isfin2  9322
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