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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdceqi | Unicode version |
Description: A class equal to a bounded one is bounded. Note the use of ax-ext 2099. See also bdceqir 12969. (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdceqi.min | BOUNDED |
bdceqi.maj |
Ref | Expression |
---|---|
bdceqi | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdceqi.min | . 2 BOUNDED | |
2 | bdceqi.maj | . . 3 | |
3 | 2 | bdceq 12967 | . 2 BOUNDED BOUNDED |
4 | 1, 3 | mpbi 144 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wceq 1316 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-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 ax-bd0 12938 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 df-bdc 12966 |
This theorem is referenced by: bdceqir 12969 bds 12976 bdcuni 13001 |
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