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Mirrors > Home > ILE Home > Th. List > Mathboxes > df-bdc | GIF version |
Description: Define a bounded class as one such that membership in this class is a bounded formula. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
df-bdc | ⊢ (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | 1 | wbdc 13426 | . 2 wff BOUNDED 𝐴 |
3 | vx | . . . . . 6 setvar 𝑥 | |
4 | 3 | cv 1334 | . . . . 5 class 𝑥 |
5 | 4, 1 | wcel 2128 | . . . 4 wff 𝑥 ∈ 𝐴 |
6 | 5 | wbd 13398 | . . 3 wff BOUNDED 𝑥 ∈ 𝐴 |
7 | 6, 3 | wal 1333 | . 2 wff ∀𝑥BOUNDED 𝑥 ∈ 𝐴 |
8 | 2, 7 | wb 104 | 1 wff (BOUNDED 𝐴 ↔ ∀𝑥BOUNDED 𝑥 ∈ 𝐴) |
Colors of variables: wff set class |
This definition is referenced by: bdceq 13428 bdel 13431 bdelir 13433 |
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