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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnulALT | Unicode version |
Description: Alternate proof of bdcnul 12990. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 12969, or use the corresponding characterizations of its elements followed by bdelir 12972. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bdcnulALT | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcvv 12982 | . . 3 BOUNDED | |
2 | 1, 1 | bdcdif 12986 | . 2 BOUNDED |
3 | df-nul 3334 | . 2 | |
4 | 2, 3 | bdceqir 12969 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: cvv 2660 cdif 3038 c0 3333 BOUNDED wbdc 12965 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 ax-bd0 12938 ax-bdim 12939 ax-bdan 12940 ax-bdn 12942 ax-bdeq 12945 ax-bdsb 12947 |
This theorem depends on definitions: df-bi 116 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 df-dif 3043 df-nul 3334 df-bdc 12966 |
This theorem is referenced by: (None) |
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