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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 8937 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 |
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nnindALT.5 |
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nnindALT.1 |
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nnindALT.2 |
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nnindALT.3 |
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nnindALT.4 |
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Ref | Expression |
---|---|
nnindALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnindALT.1 |
. 2
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2 | nnindALT.2 |
. 2
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3 | nnindALT.3 |
. 2
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4 | nnindALT.4 |
. 2
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5 | nnindALT.5 |
. 2
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6 | nnindALT.6 |
. 2
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7 | 1, 2, 3, 4, 5, 6 | nnind 8937 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4123 ax-cnex 7904 ax-resscn 7905 ax-1re 7907 ax-addrcl 7910 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-iota 5180 df-fv 5226 df-ov 5880 df-inn 8922 |
This theorem is referenced by: (None) |
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