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Mirrors > Home > ILE Home > Th. List > rspc3v | Unicode version |
Description: 3-variable restricted specialization, using implicit substitution. (Contributed by NM, 10-May-2005.) |
Ref | Expression |
---|---|
rspc3v.1 | |
rspc3v.2 | |
rspc3v.3 |
Ref | Expression |
---|---|
rspc3v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc3v.1 | . . . . 5 | |
2 | 1 | ralbidv 2326 | . . . 4 |
3 | rspc3v.2 | . . . . 5 | |
4 | 3 | ralbidv 2326 | . . . 4 |
5 | 2, 4 | rspc2v 2662 | . . 3 |
6 | rspc3v.3 | . . . 4 | |
7 | 6 | rspcv 2652 | . . 3 |
8 | 5, 7 | sylan9 389 | . 2 |
9 | 8 | 3impa 1099 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wceq 1243 wcel 1393 wral 2306 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 |
This theorem is referenced by: swopolem 4042 isopolem 5461 isosolem 5463 caovassg 5659 caovcang 5662 caovordig 5666 caovordg 5668 caovdig 5675 caovdirg 5678 caoftrn 5736 |
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