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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnul | GIF version |
Description: The empty class is bounded. See also bdcnulALT 15055. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdcnul | ⊢ BOUNDED ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3441 | . . 3 ⊢ ¬ 𝑥 ∈ ∅ | |
2 | 1 | bdnth 15023 | . 2 ⊢ BOUNDED 𝑥 ∈ ∅ |
3 | 2 | bdelir 15036 | 1 ⊢ BOUNDED ∅ |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 ∅c0 3437 BOUNDED wbdc 15029 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-bd0 15002 ax-bdim 15003 ax-bdn 15006 ax-bdeq 15009 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-dif 3146 df-nul 3438 df-bdc 15030 |
This theorem is referenced by: bdeq0 15056 |
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