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Mirrors > Home > ILE Home > Th. List > Mathboxes > peano5set | Unicode version |
Description: Version of peano5 4339 when is assumed to be a set, allowing a proof from the core axioms of CZF. (Contributed by BJ, 19-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
peano5set |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omind 10729 | . . . . 5 Ind | |
2 | bj-indind 10727 | . . . . 5 Ind Ind | |
3 | 1, 2 | mpan 414 | . . . 4 Ind |
4 | bj-omssind 10730 | . . . . 5 Ind | |
5 | 4 | imp 122 | . . . 4 Ind |
6 | 3, 5 | sylan2 280 | . . 3 |
7 | inss2 3187 | . . 3 | |
8 | 6, 7 | syl6ss 3011 | . 2 |
9 | 8 | ex 113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wcel 1433 wral 2348 cin 2972 wss 2973 c0 3251 csuc 4120 com 4331 Ind wind 10721 |
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-in1 576 ax-in2 577 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-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-nul 3904 ax-pr 3964 ax-un 4188 ax-bd0 10604 ax-bdor 10607 ax-bdex 10610 ax-bdeq 10611 ax-bdel 10612 ax-bdsb 10613 ax-bdsep 10675 |
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-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-sn 3404 df-pr 3405 df-uni 3602 df-int 3637 df-suc 4126 df-iom 4332 df-bdc 10632 df-bj-ind 10722 |
This theorem is referenced by: bdpeano5 10738 speano5 10739 |
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