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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 9295 | . 2 wff BOUNDED A |
3 | vx | . . . . . 6 setvar x | |
4 | 3 | cv 1241 | . . . . 5 class x |
5 | 4, 1 | wcel 1390 | . . . 4 wff x ∈ A |
6 | 5 | wbd 9267 | . . 3 wff BOUNDED x ∈ A |
7 | 6, 3 | wal 1240 | . 2 wff ∀xBOUNDED x ∈ A |
8 | 2, 7 | wb 98 | 1 wff (BOUNDED A ↔ ∀xBOUNDED x ∈ A) |
Colors of variables: wff set class |
This definition is referenced by: bdceq 9297 bdel 9300 bdelir 9302 |
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