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Definition df-fin5 9055
Description: A set is V-finite iff it behaves finitely under +𝑐. Definition V of [Levy58] p. 3. (Contributed by Stefan O'Rear, 12-Nov-2014.)
Assertion
Ref Expression
df-fin5 FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))}

Detailed syntax breakdown of Definition df-fin5
StepHypRef Expression
1 cfin5 9048 . 2 class FinV
2 vx . . . . . 6 setvar 𝑥
32cv 1479 . . . . 5 class 𝑥
4 c0 3891 . . . . 5 class
53, 4wceq 1480 . . . 4 wff 𝑥 = ∅
6 ccda 8933 . . . . . 6 class +𝑐
73, 3, 6co 6604 . . . . 5 class (𝑥 +𝑐 𝑥)
8 csdm 7898 . . . . 5 class
93, 7, 8wbr 4613 . . . 4 wff 𝑥 ≺ (𝑥 +𝑐 𝑥)
105, 9wo 383 . . 3 wff (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))
1110, 2cab 2607 . 2 class {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))}
121, 11wceq 1480 1 wff FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))}
Colors of variables: wff setvar class
This definition is referenced by:  isfin5  9065
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