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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnulALT | Unicode version |
Description: Alternate proof of bdcnul 12022. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 12001, or use the corresponding characterizations of its elements followed by bdelir 12004. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bdcnulALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcvv 12014 |
. . 3
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2 | 1, 1 | bdcdif 12018 |
. 2
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3 | df-nul 3288 |
. 2
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4 | 2, 3 | bdceqir 12001 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1382 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-ext 2071 ax-bd0 11970 ax-bdim 11971 ax-bdan 11972 ax-bdn 11974 ax-bdeq 11977 ax-bdsb 11979 |
This theorem depends on definitions: df-bi 116 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-v 2622 df-dif 3002 df-nul 3288 df-bdc 11998 |
This theorem is referenced by: (None) |
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