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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 13909 | . . . 4 BOUNDED | |
2 | bdcpr 13906 | . . . . . . 7 BOUNDED | |
3 | 2 | bdss 13899 | . . . . . 6 BOUNDED |
4 | ax-bdel 13856 | . . . . . . . 8 BOUNDED | |
5 | ax-bdel 13856 | . . . . . . . 8 BOUNDED | |
6 | 4, 5 | ax-bdan 13850 | . . . . . . 7 BOUNDED |
7 | vex 2733 | . . . . . . . . . . 11 | |
8 | 7 | prid1 3689 | . . . . . . . . . 10 |
9 | ssel 3141 | . . . . . . . . . 10 | |
10 | 8, 9 | mpi 15 | . . . . . . . . 9 |
11 | vex 2733 | . . . . . . . . . . 11 | |
12 | 11 | prid2 3690 | . . . . . . . . . 10 |
13 | ssel 3141 | . . . . . . . . . 10 | |
14 | 12, 13 | mpi 15 | . . . . . . . . 9 |
15 | 10, 14 | jca 304 | . . . . . . . 8 |
16 | prssi 3738 | . . . . . . . 8 | |
17 | 15, 16 | impbii 125 | . . . . . . 7 |
18 | 6, 17 | bd0r 13860 | . . . . . 6 BOUNDED |
19 | 3, 18 | ax-bdan 13850 | . . . . 5 BOUNDED |
20 | eqss 3162 | . . . . 5 | |
21 | 19, 20 | bd0r 13860 | . . . 4 BOUNDED |
22 | 1, 21 | ax-bdor 13851 | . . 3 BOUNDED |
23 | vex 2733 | . . . 4 | |
24 | 23, 7, 11 | elop 4216 | . . 3 |
25 | 22, 24 | bd0r 13860 | . 2 BOUNDED |
26 | 25 | bdelir 13882 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 703 wceq 1348 wcel 2141 wss 3121 csn 3583 cpr 3584 cop 3586 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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-bd0 13848 ax-bdan 13850 ax-bdor 13851 ax-bdal 13853 ax-bdeq 13855 ax-bdel 13856 ax-bdsb 13857 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-pr 3590 df-op 3592 df-bdc 13876 |
This theorem is referenced by: (None) |
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