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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 9942 | . . . . . . . 8 BOUNDED |
3 | ax-bdel 9941 | . . . . . . . 8 BOUNDED | |
4 | 2, 3 | ax-bdim 9934 | . . . . . . 7 BOUNDED |
5 | 4 | ax-bdal 9938 | . . . . . 6 BOUNDED |
6 | df-ral 2311 | . . . . . . . . 9 | |
7 | impexp 250 | . . . . . . . . . . 11 | |
8 | 7 | bicomi 123 | . . . . . . . . . 10 |
9 | 8 | albii 1359 | . . . . . . . . 9 |
10 | 6, 9 | bitri 173 | . . . . . . . 8 |
11 | sban 1829 | . . . . . . . . . . . 12 | |
12 | clelsb3 2142 | . . . . . . . . . . . . 13 | |
13 | 12 | anbi1i 431 | . . . . . . . . . . . 12 |
14 | 11, 13 | bitri 173 | . . . . . . . . . . 11 |
15 | 14 | bicomi 123 | . . . . . . . . . 10 |
16 | 15 | imbi1i 227 | . . . . . . . . 9 |
17 | 16 | albii 1359 | . . . . . . . 8 |
18 | 10, 17 | bitri 173 | . . . . . . 7 |
19 | df-clab 2027 | . . . . . . . . . 10 | |
20 | 19 | bicomi 123 | . . . . . . . . 9 |
21 | 20 | imbi1i 227 | . . . . . . . 8 |
22 | 21 | albii 1359 | . . . . . . 7 |
23 | 18, 22 | bitri 173 | . . . . . 6 |
24 | 5, 23 | bd0 9944 | . . . . 5 BOUNDED |
25 | 24 | bdcab 9969 | . . . 4 BOUNDED |
26 | df-int 3616 | . . . 4 | |
27 | 25, 26 | bdceqir 9964 | . . 3 BOUNDED |
28 | bdcriota.ex | . . . . 5 | |
29 | df-reu 2313 | . . . . 5 | |
30 | 28, 29 | mpbi 133 | . . . 4 |
31 | iotaint 4880 | . . . 4 | |
32 | 30, 31 | ax-mp 7 | . . 3 |
33 | 27, 32 | bdceqir 9964 | . 2 BOUNDED |
34 | df-riota 5468 | . 2 | |
35 | 33, 34 | bdceqir 9964 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wceq 1243 wcel 1393 wsb 1645 weu 1900 cab 2026 wral 2306 wreu 2308 cint 3615 cio 4865 crio 5467 BOUNDED wbd 9932 BOUNDED wbdc 9960 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-bd0 9933 ax-bdim 9934 ax-bdal 9938 ax-bdel 9941 ax-bdsb 9942 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-sn 3381 df-pr 3382 df-uni 3581 df-int 3616 df-iota 4867 df-riota 5468 df-bdc 9961 |
This theorem is referenced by: (None) |
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