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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 2435 | . . . 4 |
3 | rspc3v.2 | . . . . 5 | |
4 | 3 | ralbidv 2435 | . . . 4 |
5 | 2, 4 | rspc2v 2797 | . . 3 |
6 | rspc3v.3 | . . . 4 | |
7 | 6 | rspcv 2780 | . . 3 |
8 | 5, 7 | sylan9 406 | . 2 |
9 | 8 | 3impa 1176 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wcel 1480 wral 2414 |
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 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 |
This theorem is referenced by: swopolem 4222 isopolem 5716 isosolem 5718 caovassg 5922 caovcang 5925 caovordig 5929 caovordg 5931 caovdig 5938 caovdirg 5941 caoftrn 6000 psmettri2 12486 xmettri2 12519 |
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