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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdcriota | Unicode version |
Description: A class given by a restricted definition binder is bounded, under the given hypotheses. (Contributed by BJ, 24-Nov-2019.) |
Ref | Expression |
---|---|
bdcriota.bd | BOUNDED |
bdcriota.ex |
Ref | Expression |
---|---|
bdcriota | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcriota.bd | . . . . . . . . 9 BOUNDED | |
2 | 1 | ax-bdsb 10613 | . . . . . . . 8 BOUNDED |
3 | ax-bdel 10612 | . . . . . . . 8 BOUNDED | |
4 | 2, 3 | ax-bdim 10605 | . . . . . . 7 BOUNDED |
5 | 4 | ax-bdal 10609 | . . . . . 6 BOUNDED |
6 | df-ral 2353 | . . . . . . . . 9 | |
7 | impexp 259 | . . . . . . . . . . 11 | |
8 | 7 | bicomi 130 | . . . . . . . . . 10 |
9 | 8 | albii 1399 | . . . . . . . . 9 |
10 | 6, 9 | bitri 182 | . . . . . . . 8 |
11 | sban 1870 | . . . . . . . . . . . 12 | |
12 | clelsb3 2183 | . . . . . . . . . . . . 13 | |
13 | 12 | anbi1i 445 | . . . . . . . . . . . 12 |
14 | 11, 13 | bitri 182 | . . . . . . . . . . 11 |
15 | 14 | bicomi 130 | . . . . . . . . . 10 |
16 | 15 | imbi1i 236 | . . . . . . . . 9 |
17 | 16 | albii 1399 | . . . . . . . 8 |
18 | 10, 17 | bitri 182 | . . . . . . 7 |
19 | df-clab 2068 | . . . . . . . . . 10 | |
20 | 19 | bicomi 130 | . . . . . . . . 9 |
21 | 20 | imbi1i 236 | . . . . . . . 8 |
22 | 21 | albii 1399 | . . . . . . 7 |
23 | 18, 22 | bitri 182 | . . . . . 6 |
24 | 5, 23 | bd0 10615 | . . . . 5 BOUNDED |
25 | 24 | bdcab 10640 | . . . 4 BOUNDED |
26 | df-int 3637 | . . . 4 | |
27 | 25, 26 | bdceqir 10635 | . . 3 BOUNDED |
28 | bdcriota.ex | . . . . 5 | |
29 | df-reu 2355 | . . . . 5 | |
30 | 28, 29 | mpbi 143 | . . . 4 |
31 | iotaint 4900 | . . . 4 | |
32 | 30, 31 | ax-mp 7 | . . 3 |
33 | 27, 32 | bdceqir 10635 | . 2 BOUNDED |
34 | df-riota 5488 | . 2 | |
35 | 33, 34 | bdceqir 10635 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wal 1282 wceq 1284 wcel 1433 wsb 1685 weu 1941 cab 2067 wral 2348 wreu 2350 cint 3636 cio 4885 crio 5487 BOUNDED wbd 10603 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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-bd0 10604 ax-bdim 10605 ax-bdal 10609 ax-bdel 10612 ax-bdsb 10613 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-reu 2355 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-sn 3404 df-pr 3405 df-uni 3602 df-int 3637 df-iota 4887 df-riota 5488 df-bdc 10632 |
This theorem is referenced by: (None) |
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