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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnul | GIF version |
Description: The empty class is bounded. See also bdcnulALT 11640. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcnul | ⊢ BOUNDED ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3290 | . . 3 ⊢ ¬ 𝑥 ∈ ∅ | |
2 | 1 | bdnth 11608 | . 2 ⊢ BOUNDED 𝑥 ∈ ∅ |
3 | 2 | bdelir 11621 | 1 ⊢ BOUNDED ∅ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 ∅c0 3286 BOUNDED wbdc 11614 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-bd0 11587 ax-bdim 11588 ax-bdn 11591 ax-bdeq 11594 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-v 2621 df-dif 3001 df-nul 3287 df-bdc 11615 |
This theorem is referenced by: bdeq0 11641 |
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