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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 13005 | . . . 4 BOUNDED | |
2 | 1 | bdss 12989 | . . 3 BOUNDED |
3 | bdcv 12973 | . . . . . . 7 BOUNDED | |
4 | 3 | bdss 12989 | . . . . . 6 BOUNDED |
5 | 3 | bdsnss 12998 | . . . . . 6 BOUNDED |
6 | 4, 5 | ax-bdan 12940 | . . . . 5 BOUNDED |
7 | unss 3220 | . . . . 5 | |
8 | 6, 7 | bd0 12949 | . . . 4 BOUNDED |
9 | df-suc 4263 | . . . . 5 | |
10 | 9 | sseq1i 3093 | . . . 4 |
11 | 8, 10 | bd0r 12950 | . . 3 BOUNDED |
12 | 2, 11 | ax-bdan 12940 | . 2 BOUNDED |
13 | eqss 3082 | . 2 | |
14 | 12, 13 | bd0r 12950 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1316 cun 3039 wss 3041 csn 3497 csuc 4257 BOUNDED wbd 12937 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-bd0 12938 ax-bdan 12940 ax-bdor 12941 ax-bdal 12943 ax-bdeq 12945 ax-bdel 12946 ax-bdsb 12947 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-suc 4263 df-bdc 12966 |
This theorem is referenced by: bj-bdsucel 13007 bj-nn0suc0 13075 |
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