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Mirrors > Home > ILE Home > Th. List > nnindALT | Unicode version |
Description: Principle of Mathematical
Induction (inference schema). The last four
hypotheses give us the substitution instances we need; the first two are
the induction step and the basis.
This ALT version of nnind 8704 has a different hypothesis order. It may be easier to use with the metamath program's Proof Assistant, because "MM-PA> assign last" will be applied to the substitution instances first. We may eventually use this one as the official version. You may use either version. After the proof is complete, the ALT version can be changed to the non-ALT version with "MM-PA> minimize nnind /allow". (Contributed by NM, 7-Dec-2005.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
nnindALT.6 | |
nnindALT.5 | |
nnindALT.1 | |
nnindALT.2 | |
nnindALT.3 | |
nnindALT.4 |
Ref | Expression |
---|---|
nnindALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnindALT.1 | . 2 | |
2 | nnindALT.2 | . 2 | |
3 | nnindALT.3 | . 2 | |
4 | nnindALT.4 | . 2 | |
5 | nnindALT.5 | . 2 | |
6 | nnindALT.6 | . 2 | |
7 | 1, 2, 3, 4, 5, 6 | nnind 8704 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 (class class class)co 5742 c1 7589 caddc 7591 cn 8688 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1re 7682 ax-addrcl 7685 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-inn 8689 |
This theorem is referenced by: (None) |
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