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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 8867 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 8867 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wcel 2135 (class class class)co 5839 c1 7748 caddc 7750 cn 8851 |
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 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-ext 2146 ax-sep 4097 ax-cnex 7838 ax-resscn 7839 ax-1re 7841 ax-addrcl 7844 |
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-un 3118 df-in 3120 df-ss 3127 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-int 3822 df-br 3980 df-iota 5150 df-fv 5193 df-ov 5842 df-inn 8852 |
This theorem is referenced by: (None) |
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