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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdeqsuc | Unicode version |
Description: Boundedness of the formula expressing that a setvar is equal to the successor of another. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bdeqsuc | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdcsuc 10671 | . . . 4 BOUNDED | |
2 | 1 | bdss 10655 | . . 3 BOUNDED |
3 | bdcv 10639 | . . . . . . 7 BOUNDED | |
4 | 3 | bdss 10655 | . . . . . 6 BOUNDED |
5 | 3 | bdsnss 10664 | . . . . . 6 BOUNDED |
6 | 4, 5 | ax-bdan 10606 | . . . . 5 BOUNDED |
7 | unss 3146 | . . . . 5 | |
8 | 6, 7 | bd0 10615 | . . . 4 BOUNDED |
9 | df-suc 4126 | . . . . 5 | |
10 | 9 | sseq1i 3023 | . . . 4 |
11 | 8, 10 | bd0r 10616 | . . 3 BOUNDED |
12 | 2, 11 | ax-bdan 10606 | . 2 BOUNDED |
13 | eqss 3014 | . 2 | |
14 | 12, 13 | bd0r 10616 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 cun 2971 wss 2973 csn 3398 csuc 4120 BOUNDED wbd 10603 |
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-bdan 10606 ax-bdor 10607 ax-bdal 10609 ax-bdeq 10611 ax-bdel 10612 ax-bdsb 10613 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-suc 4126 df-bdc 10632 |
This theorem is referenced by: bj-bdsucel 10673 bj-nn0suc0 10745 |
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