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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnulALT | Unicode version |
Description: Alternate proof of bdcnul 13694. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13673, or use the corresponding characterizations of its elements followed by bdelir 13676. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bdcnulALT | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcvv 13686 | . . 3 BOUNDED | |
2 | 1, 1 | bdcdif 13690 | . 2 BOUNDED |
3 | df-nul 3409 | . 2 | |
4 | 2, 3 | bdceqir 13673 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: cvv 2725 cdif 3112 c0 3408 BOUNDED wbdc 13669 |
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 1435 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-ext 2147 ax-bd0 13642 ax-bdim 13643 ax-bdan 13644 ax-bdn 13646 ax-bdeq 13649 ax-bdsb 13651 |
This theorem depends on definitions: df-bi 116 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-v 2727 df-dif 3117 df-nul 3409 df-bdc 13670 |
This theorem is referenced by: (None) |
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