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Mirrors > Home > NFE 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 2634 | . . . 4 |
3 | rspc3v.2 | . . . . 5 | |
4 | 3 | ralbidv 2634 | . . . 4 |
5 | 2, 4 | rspc2v 2961 | . . 3 |
6 | rspc3v.3 | . . . 4 | |
7 | 6 | rspcv 2951 | . . 3 |
8 | 5, 7 | sylan9 638 | . 2 |
9 | 8 | 3impa 1146 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 w3a 934 wceq 1642 wcel 1710 wral 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3an 936 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 |
This theorem is referenced by: caovassg 5626 caovdig 5632 caovdirg 5633 trd 5921 |
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