Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > peano5set | Unicode version |
Description: Version of peano5 4570 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 13668 | . . . . 5 Ind | |
2 | bj-indind 13666 | . . . . 5 Ind Ind | |
3 | 1, 2 | mpan 421 | . . . 4 Ind |
4 | bj-omssind 13669 | . . . . 5 Ind | |
5 | 4 | imp 123 | . . . 4 Ind |
6 | 3, 5 | sylan2 284 | . . 3 |
7 | inss2 3339 | . . 3 | |
8 | 6, 7 | sstrdi 3150 | . 2 |
9 | 8 | ex 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 2135 wral 2442 cin 3111 wss 3112 c0 3405 csuc 4338 com 4562 Ind wind 13660 |
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 604 ax-in2 605 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-13 2137 ax-14 2138 ax-ext 2146 ax-nul 4103 ax-pr 4182 ax-un 4406 ax-bd0 13547 ax-bdor 13550 ax-bdex 13553 ax-bdeq 13554 ax-bdel 13555 ax-bdsb 13556 ax-bdsep 13618 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-nul 3406 df-sn 3577 df-pr 3578 df-uni 3785 df-int 3820 df-suc 4344 df-iom 4563 df-bdc 13575 df-bj-ind 13661 |
This theorem is referenced by: bdpeano5 13677 speano5 13678 |
Copyright terms: Public domain | W3C validator |