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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 10661 | . . 3 BOUNDED | |
2 | bdcsn 10661 | . . 3 BOUNDED | |
3 | 1, 2 | bdcun 10653 | . 2 BOUNDED |
4 | df-pr 3405 | . 2 | |
5 | 3, 4 | bdceqir 10635 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: cun 2971 csn 3398 cpr 3399 BOUNDED wbdc 10631 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-4 1440 ax-17 1459 ax-ial 1467 ax-ext 2063 ax-bd0 10604 ax-bdor 10607 ax-bdeq 10611 ax-bdsb 10613 |
This theorem depends on definitions: df-bi 115 df-clab 2068 df-cleq 2074 df-clel 2077 df-un 2977 df-sn 3404 df-pr 3405 df-bdc 10632 |
This theorem is referenced by: bdctp 10663 bdop 10666 |
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