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Mirrors > Home > ILE Home > Th. List > Mathboxes > peano5set | Unicode version |
Description: Version of peano5 4507 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 13121 | . . . . 5 Ind | |
2 | bj-indind 13119 | . . . . 5 Ind Ind | |
3 | 1, 2 | mpan 420 | . . . 4 Ind |
4 | bj-omssind 13122 | . . . . 5 Ind | |
5 | 4 | imp 123 | . . . 4 Ind |
6 | 3, 5 | sylan2 284 | . . 3 |
7 | inss2 3292 | . . 3 | |
8 | 6, 7 | sstrdi 3104 | . 2 |
9 | 8 | ex 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 wral 2414 cin 3065 wss 3066 c0 3358 csuc 4282 com 4499 Ind wind 13113 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-nul 4049 ax-pr 4126 ax-un 4350 ax-bd0 13000 ax-bdor 13003 ax-bdex 13006 ax-bdeq 13007 ax-bdel 13008 ax-bdsb 13009 ax-bdsep 13071 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-rab 2423 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-sn 3528 df-pr 3529 df-uni 3732 df-int 3767 df-suc 4288 df-iom 4500 df-bdc 13028 df-bj-ind 13114 |
This theorem is referenced by: bdpeano5 13130 speano5 13131 |
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