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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdceqir | Unicode version |
Description: A class equal to a bounded one is bounded. Stated with a commuted (compared with bdceqi 13878) equality in the hypothesis, to work better with definitions ( is the definiendum that one wants to prove bounded; see comment of bd0r 13860). (Contributed by BJ, 3-Oct-2019.) |
Ref | Expression |
---|---|
bdceqir.min | BOUNDED |
bdceqir.maj |
Ref | Expression |
---|---|
bdceqir | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdceqir.min | . 2 BOUNDED | |
2 | bdceqir.maj | . . 3 | |
3 | 2 | eqcomi 2174 | . 2 |
4 | 1, 3 | bdceqi 13878 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wceq 1348 BOUNDED wbdc 13875 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 ax-bd0 13848 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 df-clel 2166 df-bdc 13876 |
This theorem is referenced by: bdcrab 13887 bdccsb 13895 bdcdif 13896 bdcun 13897 bdcin 13898 bdcnulALT 13901 bdcpw 13904 bdcsn 13905 bdcpr 13906 bdctp 13907 bdcuni 13911 bdcint 13912 bdciun 13913 bdciin 13914 bdcsuc 13915 bdcriota 13918 |
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