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Mirrors > Home > ILE Home > Th. List > finds1 | Unicode version |
Description: Principle of Finite Induction (inference schema), using implicit substitutions. The first three hypotheses establish the substitutions we need. The last two are the basis and the induction step. Theorem Schema 22 of [Suppes] p. 136. (Contributed by NM, 22-Mar-2006.) |
Ref | Expression |
---|---|
finds1.1 |
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finds1.2 |
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finds1.3 |
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finds1.4 |
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finds1.5 |
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Ref | Expression |
---|---|
finds1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2177 |
. 2
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2 | finds1.1 |
. . 3
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3 | finds1.2 |
. . 3
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4 | finds1.3 |
. . 3
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5 | finds1.4 |
. . . 4
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6 | 5 | a1i 9 |
. . 3
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7 | finds1.5 |
. . . 4
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8 | 7 | a1d 22 |
. . 3
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9 | 2, 3, 4, 6, 8 | finds2 4602 |
. 2
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10 | 1, 9 | mpi 15 |
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-in1 614 ax-in2 615 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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-nul 4131 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-iinf 4589 |
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-v 2741 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-pw 3579 df-sn 3600 df-pr 3601 df-uni 3812 df-int 3847 df-suc 4373 df-iom 4592 |
This theorem is referenced by: findcard 6890 findcard2 6891 findcard2s 6892 |
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