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Mirrors > Home > ILE Home > Th. List > tfis2f | Unicode version |
Description: Transfinite Induction Schema, using implicit substitution. (Contributed by NM, 18-Aug-1994.) |
Ref | Expression |
---|---|
tfis2f.1 | |
tfis2f.2 | |
tfis2f.3 |
Ref | Expression |
---|---|
tfis2f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfis2f.1 | . . . . 5 | |
2 | tfis2f.2 | . . . . 5 | |
3 | 1, 2 | sbie 1764 | . . . 4 |
4 | 3 | ralbii 2441 | . . 3 |
5 | tfis2f.3 | . . 3 | |
6 | 4, 5 | syl5bi 151 | . 2 |
7 | 6 | tfis 4497 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wnf 1436 wcel 1480 wsb 1735 wral 2416 con0 4285 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-rab 2425 df-v 2688 df-in 3077 df-ss 3084 df-uni 3737 df-tr 4027 df-iord 4288 df-on 4290 |
This theorem is referenced by: tfis2 4499 tfri3 6264 |
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