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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 13545 | . . . . . . . 8 BOUNDED |
3 | ax-bdel 13544 | . . . . . . . 8 BOUNDED | |
4 | 2, 3 | ax-bdim 13537 | . . . . . . 7 BOUNDED |
5 | 4 | ax-bdal 13541 | . . . . . 6 BOUNDED |
6 | df-ral 2447 | . . . . . . . . 9 | |
7 | impexp 261 | . . . . . . . . . . 11 | |
8 | 7 | bicomi 131 | . . . . . . . . . 10 |
9 | 8 | albii 1457 | . . . . . . . . 9 |
10 | 6, 9 | bitri 183 | . . . . . . . 8 |
11 | sban 1942 | . . . . . . . . . . . 12 | |
12 | clelsb3 2269 | . . . . . . . . . . . . 13 | |
13 | 12 | anbi1i 454 | . . . . . . . . . . . 12 |
14 | 11, 13 | bitri 183 | . . . . . . . . . . 11 |
15 | 14 | bicomi 131 | . . . . . . . . . 10 |
16 | 15 | imbi1i 237 | . . . . . . . . 9 |
17 | 16 | albii 1457 | . . . . . . . 8 |
18 | 10, 17 | bitri 183 | . . . . . . 7 |
19 | df-clab 2151 | . . . . . . . . . 10 | |
20 | 19 | bicomi 131 | . . . . . . . . 9 |
21 | 20 | imbi1i 237 | . . . . . . . 8 |
22 | 21 | albii 1457 | . . . . . . 7 |
23 | 18, 22 | bitri 183 | . . . . . 6 |
24 | 5, 23 | bd0 13547 | . . . . 5 BOUNDED |
25 | 24 | bdcab 13572 | . . . 4 BOUNDED |
26 | df-int 3819 | . . . 4 | |
27 | 25, 26 | bdceqir 13567 | . . 3 BOUNDED |
28 | bdcriota.ex | . . . . 5 | |
29 | df-reu 2449 | . . . . 5 | |
30 | 28, 29 | mpbi 144 | . . . 4 |
31 | iotaint 5160 | . . . 4 | |
32 | 30, 31 | ax-mp 5 | . . 3 |
33 | 27, 32 | bdceqir 13567 | . 2 BOUNDED |
34 | df-riota 5792 | . 2 | |
35 | 33, 34 | bdceqir 13567 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1340 wceq 1342 wsb 1749 weu 2013 wcel 2135 cab 2150 wral 2442 wreu 2444 cint 3818 cio 5145 crio 5791 BOUNDED wbd 13535 BOUNDED wbdc 13563 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 ax-bd0 13536 ax-bdim 13537 ax-bdal 13541 ax-bdel 13544 ax-bdsb 13545 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-sn 3576 df-pr 3577 df-uni 3784 df-int 3819 df-iota 5147 df-riota 5792 df-bdc 13564 |
This theorem is referenced by: (None) |
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