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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnul | GIF version |
Description: The empty class is bounded. See also bdcnulALT 13512. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcnul | ⊢ BOUNDED ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3399 | . . 3 ⊢ ¬ 𝑥 ∈ ∅ | |
2 | 1 | bdnth 13480 | . 2 ⊢ BOUNDED 𝑥 ∈ ∅ |
3 | 2 | bdelir 13493 | 1 ⊢ BOUNDED ∅ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2128 ∅c0 3395 BOUNDED wbdc 13486 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-bd0 13459 ax-bdim 13460 ax-bdn 13463 ax-bdeq 13466 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-nul 3396 df-bdc 13487 |
This theorem is referenced by: bdeq0 13513 |
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