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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 2692 | . . 3 ⊢ 𝑥 ∈ V | |
2 | 1 | bdth 13200 | . 2 ⊢ BOUNDED 𝑥 ∈ V |
3 | 2 | bdelir 13216 | 1 ⊢ BOUNDED V |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1481 Vcvv 2689 BOUNDED wbdc 13209 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 ax-bd0 13182 ax-bdim 13183 ax-bdeq 13189 |
This theorem depends on definitions: df-bi 116 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 df-bdc 13210 |
This theorem is referenced by: bdcnulALT 13235 |
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