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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcvv | GIF version |
Description: The universal class is bounded. The formulation may sound strange, but recall that here, "bounded" means "Δ0". (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcvv | ⊢ BOUNDED V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2755 | . . 3 ⊢ 𝑥 ∈ V | |
2 | 1 | bdth 15061 | . 2 ⊢ BOUNDED 𝑥 ∈ V |
3 | 2 | bdelir 15077 | 1 ⊢ BOUNDED V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 Vcvv 2752 BOUNDED wbdc 15070 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-ext 2171 ax-bd0 15043 ax-bdim 15044 ax-bdeq 15050 |
This theorem depends on definitions: df-bi 117 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 df-bdc 15071 |
This theorem is referenced by: bdcnulALT 15096 |
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