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Definition df-fin5 9703
Description: A set is V-finite iff it behaves finitely under . Definition V of [Levy58] p. 3. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin5 FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥𝑥))}

Detailed syntax breakdown of Definition df-fin5
StepHypRef Expression
1 cfin5 9696 . 2 class FinV
2 vx . . . . . 6 setvar 𝑥
32cv 1529 . . . . 5 class 𝑥
4 c0 4294 . . . . 5 class
53, 4wceq 1530 . . . 4 wff 𝑥 = ∅
63, 3cdju 9319 . . . . 5 class (𝑥𝑥)
7 csdm 8500 . . . . 5 class
83, 6, 7wbr 5062 . . . 4 wff 𝑥 ≺ (𝑥𝑥)
95, 8wo 843 . . 3 wff (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥𝑥))
109, 2cab 2802 . 2 class {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥𝑥))}
111, 10wceq 1530 1 wff FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥𝑥))}
Colors of variables: wff setvar class
This definition is referenced by:  isfin5  9713
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