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Definition df-fin6 8972
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 8965 . 2 class FinVI
2 vx . . . . . 6 setvar 𝑥
32cv 1473 . . . . 5 class 𝑥
4 c2o 7418 . . . . 5 class 2𝑜
5 csdm 7817 . . . . 5 class
63, 4, 5wbr 4577 . . . 4 wff 𝑥 ≺ 2𝑜
73, 3cxp 5026 . . . . 5 class (𝑥 × 𝑥)
83, 7, 5wbr 4577 . . . 4 wff 𝑥 ≺ (𝑥 × 𝑥)
96, 8wo 381 . . 3 wff (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))
109, 2cab 2595 . 2 class {𝑥 ∣ (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))}
111, 10wceq 1474 1 wff FinVI = {𝑥 ∣ (𝑥 ≺ 2𝑜𝑥 ≺ (𝑥 × 𝑥))}
Colors of variables: wff setvar class
This definition is referenced by:  isfin6  8982
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