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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcpr | Unicode version |
Description: The pair of two setvars is bounded. (Contributed by BJ, 16-Oct-2019.) |
Ref | Expression |
---|---|
bdcpr | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsn 12995 | . . 3 BOUNDED | |
2 | bdcsn 12995 | . . 3 BOUNDED | |
3 | 1, 2 | bdcun 12987 | . 2 BOUNDED |
4 | df-pr 3504 | . 2 | |
5 | 3, 4 | bdceqir 12969 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: cun 3039 csn 3497 cpr 3498 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 ax-bdor 12941 ax-bdeq 12945 ax-bdsb 12947 |
This theorem depends on definitions: df-bi 116 df-clab 2104 df-cleq 2110 df-clel 2113 df-un 3045 df-sn 3503 df-pr 3504 df-bdc 12966 |
This theorem is referenced by: bdctp 12997 bdop 13000 |
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