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Definition df-fin3 10328

Description: A set is III-finite (weakly Dedekind finite) iff its power set is Dedekind finite. Definition III of [Levy58] p. 2. (Contributed by Stefan O'Rear, 12-Nov-2014.)

**Assertion**
Ref	Expression
df-fin3	⊢ Fin^III = {𝑥 ∣ 𝒫 𝑥 ∈ Fin^IV}

**Detailed syntax breakdown of Definition df-fin3**
Step	Hyp	Ref	Expression
1		cfin3 10321	. 2 class Fin^III
2		vx	. . . . . 6 setvar 𝑥
3	2	cv 1539	. . . . 5 class 𝑥
4	3	cpw 4600	. . . 4 class 𝒫 𝑥
5		cfin4 10320	. . . 4 class Fin^IV
6	4, 5	wcel 2108	. . 3 wff 𝒫 𝑥 ∈ Fin^IV
7	6, 2	cab 2714	. 2 class {𝑥 ∣ 𝒫 𝑥 ∈ Fin^IV}
8	1, 7	wceq 1540	1 wff Fin^III = {𝑥 ∣ 𝒫 𝑥 ∈ Fin^IV}

Colors of variables: wff setvar class

This definition is referenced by: isfin3 10336

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