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Mirrors > Home > ILE Home > Th. List > Mathboxes > ax-bdal | GIF version |
Description: A bounded universal quantification of a bounded formula is bounded. Note the disjoint variable condition on 𝑥, 𝑦. (Contributed by BJ, 25-Sep-2019.) |
Ref | Expression |
---|---|
bdal.1 | ⊢ BOUNDED 𝜑 |
Ref | Expression |
---|---|
ax-bdal | ⊢ BOUNDED ∀𝑥 ∈ 𝑦 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . . 3 wff 𝜑 | |
2 | vx | . . 3 setvar 𝑥 | |
3 | vy | . . . 4 setvar 𝑦 | |
4 | 3 | cv 1347 | . . 3 class 𝑦 |
5 | 1, 2, 4 | wral 2448 | . 2 wff ∀𝑥 ∈ 𝑦 𝜑 |
6 | 5 | wbd 13809 | 1 wff BOUNDED ∀𝑥 ∈ 𝑦 𝜑 |
Colors of variables: wff set class |
This axiom is referenced by: bdreu 13852 bdss 13861 bdcint 13874 bdciin 13876 bdcriota 13880 bj-bdind 13927 bj-nntrans 13948 |
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