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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcnulALT | Unicode version |
Description: Alternate proof of bdcnul 14913. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 14892, or use the corresponding characterizations of its elements followed by bdelir 14895. (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 14905 |
. . 3
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2 | 1, 1 | bdcdif 14909 |
. 2
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3 | df-nul 3435 |
. 2
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4 | 2, 3 | bdceqir 14892 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-ext 2169 ax-bd0 14861 ax-bdim 14862 ax-bdan 14863 ax-bdn 14865 ax-bdeq 14868 ax-bdsb 14870 |
This theorem depends on definitions: df-bi 117 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-v 2751 df-dif 3143 df-nul 3435 df-bdc 14889 |
This theorem is referenced by: (None) |
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