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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 2438 | . . . 4 |
3 | rspc3v.2 | . . . . 5 | |
4 | 3 | ralbidv 2438 | . . . 4 |
5 | 2, 4 | rspc2v 2806 | . . 3 |
6 | rspc3v.3 | . . . 4 | |
7 | 6 | rspcv 2789 | . . 3 |
8 | 5, 7 | sylan9 407 | . 2 |
9 | 8 | 3impa 1177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 963 wceq 1332 wcel 1481 wral 2417 |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-v 2691 |
This theorem is referenced by: swopolem 4235 isopolem 5731 isosolem 5733 caovassg 5937 caovcang 5940 caovordig 5944 caovordg 5946 caovdig 5953 caovdirg 5956 caoftrn 6015 psmettri2 12536 xmettri2 12569 |
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