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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 | |
finds1.2 | |
finds1.3 | |
finds1.4 | |
finds1.5 |
Ref | Expression |
---|---|
finds1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2117 | . 2 | |
2 | finds1.1 | . . 3 | |
3 | finds1.2 | . . 3 | |
4 | finds1.3 | . . 3 | |
5 | finds1.4 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | finds1.5 | . . . 4 | |
8 | 7 | a1d 22 | . . 3 |
9 | 2, 3, 4, 6, 8 | finds2 4485 | . 2 |
10 | 1, 9 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 c0 3333 csuc 4257 com 4474 |
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 588 ax-in2 589 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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-iinf 4472 |
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-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-int 3742 df-suc 4263 df-iom 4475 |
This theorem is referenced by: findcard 6750 findcard2 6751 findcard2s 6752 |
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