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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdop | Unicode version |
Description: The ordered pair of two setvars is a bounded class. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bdop | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdvsn 13072 | . . . 4 BOUNDED | |
2 | bdcpr 13069 | . . . . . . 7 BOUNDED | |
3 | 2 | bdss 13062 | . . . . . 6 BOUNDED |
4 | ax-bdel 13019 | . . . . . . . 8 BOUNDED | |
5 | ax-bdel 13019 | . . . . . . . 8 BOUNDED | |
6 | 4, 5 | ax-bdan 13013 | . . . . . . 7 BOUNDED |
7 | vex 2689 | . . . . . . . . . . 11 | |
8 | 7 | prid1 3629 | . . . . . . . . . 10 |
9 | ssel 3091 | . . . . . . . . . 10 | |
10 | 8, 9 | mpi 15 | . . . . . . . . 9 |
11 | vex 2689 | . . . . . . . . . . 11 | |
12 | 11 | prid2 3630 | . . . . . . . . . 10 |
13 | ssel 3091 | . . . . . . . . . 10 | |
14 | 12, 13 | mpi 15 | . . . . . . . . 9 |
15 | 10, 14 | jca 304 | . . . . . . . 8 |
16 | prssi 3678 | . . . . . . . 8 | |
17 | 15, 16 | impbii 125 | . . . . . . 7 |
18 | 6, 17 | bd0r 13023 | . . . . . 6 BOUNDED |
19 | 3, 18 | ax-bdan 13013 | . . . . 5 BOUNDED |
20 | eqss 3112 | . . . . 5 | |
21 | 19, 20 | bd0r 13023 | . . . 4 BOUNDED |
22 | 1, 21 | ax-bdor 13014 | . . 3 BOUNDED |
23 | vex 2689 | . . . 4 | |
24 | 23, 7, 11 | elop 4153 | . . 3 |
25 | 22, 24 | bd0r 13023 | . 2 BOUNDED |
26 | 25 | bdelir 13045 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 697 wceq 1331 wcel 1480 wss 3071 csn 3527 cpr 3528 cop 3530 BOUNDED wbdc 13038 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-bd0 13011 ax-bdan 13013 ax-bdor 13014 ax-bdal 13016 ax-bdeq 13018 ax-bdel 13019 ax-bdsb 13020 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-sn 3533 df-pr 3534 df-op 3536 df-bdc 13039 |
This theorem is referenced by: (None) |
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