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Mirrors > Home > ILE Home > Th. List > Mathboxes > speano5 | Unicode version |
Description: Version of peano5 4572 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 |
---|---|
speano5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omex 13717 | . . . 4 | |
2 | bj-inex 13682 | . . . 4 | |
3 | 1, 2 | mpan 421 | . . 3 |
4 | peano5set 13715 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | 5 | 3impib 1190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 wcel 2135 wral 2442 cvv 2724 cin 3113 wss 3114 c0 3407 csuc 4340 com 4564 |
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 4105 ax-pr 4184 ax-un 4408 ax-bd0 13588 ax-bdan 13590 ax-bdor 13591 ax-bdex 13594 ax-bdeq 13595 ax-bdel 13596 ax-bdsb 13597 ax-bdsep 13659 ax-infvn 13716 |
This theorem depends on definitions: df-bi 116 df-3an 969 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 2726 df-dif 3116 df-un 3118 df-in 3120 df-ss 3127 df-nul 3408 df-sn 3579 df-pr 3580 df-uni 3787 df-int 3822 df-suc 4346 df-iom 4565 df-bdc 13616 df-bj-ind 13702 |
This theorem is referenced by: findset 13720 |
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