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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-peano2 | Unicode version |
Description: Constructive proof of peano2 4553. Temporary note: another possibility is to simply replace sucexg 4456 with bj-sucexg 13484 in the proof of peano2 4553. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-peano2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-omind 13496 | . 2 Ind | |
2 | bj-indsuc 13490 | . 2 Ind | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2128 csuc 4325 com 4548 Ind wind 13488 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-nul 4090 ax-pr 4169 ax-un 4393 ax-bd0 13375 ax-bdor 13378 ax-bdex 13381 ax-bdeq 13382 ax-bdel 13383 ax-bdsb 13384 ax-bdsep 13446 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-nul 3395 df-sn 3566 df-pr 3567 df-uni 3773 df-int 3808 df-suc 4331 df-iom 4549 df-bdc 13403 df-bj-ind 13489 |
This theorem is referenced by: bj-nn0suc 13526 bj-nn0sucALT 13540 |
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