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Mirrors > Home > MPE Home > Th. List > df-fin5 | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
df-fin5 | ⊢ FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cfin5 8987 | . 2 class FinV | |
2 | vx | . . . . . 6 setvar 𝑥 | |
3 | 2 | cv 1474 | . . . . 5 class 𝑥 |
4 | c0 3874 | . . . . 5 class ∅ | |
5 | 3, 4 | wceq 1475 | . . . 4 wff 𝑥 = ∅ |
6 | ccda 8872 | . . . . . 6 class +𝑐 | |
7 | 3, 3, 6 | co 6549 | . . . . 5 class (𝑥 +𝑐 𝑥) |
8 | csdm 7840 | . . . . 5 class ≺ | |
9 | 3, 7, 8 | wbr 4583 | . . . 4 wff 𝑥 ≺ (𝑥 +𝑐 𝑥) |
10 | 5, 9 | wo 382 | . . 3 wff (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥)) |
11 | 10, 2 | cab 2596 | . 2 class {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))} |
12 | 1, 11 | wceq 1475 | 1 wff FinV = {𝑥 ∣ (𝑥 = ∅ ∨ 𝑥 ≺ (𝑥 +𝑐 𝑥))} |
Colors of variables: wff setvar class |
This definition is referenced by: isfin5 9004 |
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