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Definition df-fin6 9395
Description: A set is VI-finite iff it behaves finitely under ×. Definition VI of [Levy58] p. 4. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin6 FinVI = {𝑥 ∣ (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))}

Detailed syntax breakdown of Definition df-fin6
StepHypRef Expression
1 cfin6 9388 . 2 class FinVI
2 vx . . . . . 6 setvar 𝑥
32cv 1636 . . . . 5 class 𝑥
4 c2o 7788 . . . . 5 class 2𝑜
5 csdm 8189 . . . . 5 class
63, 4, 5wbr 4842 . . . 4 wff 𝑥 ≺ 2𝑜
73, 3cxp 5307 . . . . 5 class (𝑥 × 𝑥)
83, 7, 5wbr 4842 . . . 4 wff 𝑥 ≺ (𝑥 × 𝑥)
96, 8wo 865 . . 3 wff (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))
109, 2cab 2790 . 2 class {𝑥 ∣ (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))}
111, 10wceq 1637 1 wff FinVI = {𝑥 ∣ (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))}
Colors of variables: wff setvar class
This definition is referenced by:  isfin6  9405
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