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Mirrors > Home > MPE Home > Th. List > df-fin3 | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-fin3 | ⊢ FinIII = {𝑥 ∣ 𝒫 𝑥 ∈ FinIV} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfin3 9781 | . 2 class FinIII | |
2 | vx | . . . . . 6 setvar 𝑥 | |
3 | 2 | cv 1541 | . . . . 5 class 𝑥 |
4 | 3 | cpw 4488 | . . . 4 class 𝒫 𝑥 |
5 | cfin4 9780 | . . . 4 class FinIV | |
6 | 4, 5 | wcel 2114 | . . 3 wff 𝒫 𝑥 ∈ FinIV |
7 | 6, 2 | cab 2716 | . 2 class {𝑥 ∣ 𝒫 𝑥 ∈ FinIV} |
8 | 1, 7 | wceq 1542 | 1 wff FinIII = {𝑥 ∣ 𝒫 𝑥 ∈ FinIV} |
Colors of variables: wff setvar class |
This definition is referenced by: isfin3 9796 |
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