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Mirrors > Home > ILE Home > Th. List > cbvrabcsf | Unicode version |
Description: A more general version of cbvrab 2599 with no distinct variable restrictions. (Contributed by Andrew Salmon, 13-Jul-2011.) |
Ref | Expression |
---|---|
cbvralcsf.1 | |
cbvralcsf.2 | |
cbvralcsf.3 | |
cbvralcsf.4 | |
cbvralcsf.5 | |
cbvralcsf.6 |
Ref | Expression |
---|---|
cbvrabcsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . 4 | |
2 | nfcsb1v 2938 | . . . . . 6 | |
3 | 2 | nfcri 2213 | . . . . 5 |
4 | nfs1v 1856 | . . . . 5 | |
5 | 3, 4 | nfan 1497 | . . . 4 |
6 | id 19 | . . . . . 6 | |
7 | csbeq1a 2916 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2149 | . . . . 5 |
9 | sbequ12 1694 | . . . . 5 | |
10 | 8, 9 | anbi12d 456 | . . . 4 |
11 | 1, 5, 10 | cbvab 2201 | . . 3 |
12 | nfcv 2219 | . . . . . . 7 | |
13 | cbvralcsf.1 | . . . . . . 7 | |
14 | 12, 13 | nfcsb 2940 | . . . . . 6 |
15 | 14 | nfcri 2213 | . . . . 5 |
16 | cbvralcsf.3 | . . . . . 6 | |
17 | 16 | nfsb 1863 | . . . . 5 |
18 | 15, 17 | nfan 1497 | . . . 4 |
19 | nfv 1461 | . . . 4 | |
20 | id 19 | . . . . . 6 | |
21 | csbeq1 2911 | . . . . . . 7 | |
22 | df-csb 2909 | . . . . . . . 8 | |
23 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
24 | 23 | nfcri 2213 | . . . . . . . . . . 11 |
25 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
26 | 25 | eleq2d 2148 | . . . . . . . . . . 11 |
27 | 24, 26 | sbie 1714 | . . . . . . . . . 10 |
28 | sbsbc 2819 | . . . . . . . . . 10 | |
29 | 27, 28 | bitr3i 184 | . . . . . . . . 9 |
30 | 29 | abbi2i 2193 | . . . . . . . 8 |
31 | 22, 30 | eqtr4i 2104 | . . . . . . 7 |
32 | 21, 31 | syl6eq 2129 | . . . . . 6 |
33 | 20, 32 | eleq12d 2149 | . . . . 5 |
34 | sbequ 1761 | . . . . . 6 | |
35 | cbvralcsf.4 | . . . . . . 7 | |
36 | cbvralcsf.6 | . . . . . . 7 | |
37 | 35, 36 | sbie 1714 | . . . . . 6 |
38 | 34, 37 | syl6bb 194 | . . . . 5 |
39 | 33, 38 | anbi12d 456 | . . . 4 |
40 | 18, 19, 39 | cbvab 2201 | . . 3 |
41 | 11, 40 | eqtri 2101 | . 2 |
42 | df-rab 2357 | . 2 | |
43 | df-rab 2357 | . 2 | |
44 | 41, 42, 43 | 3eqtr4i 2111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wcel 1433 wsb 1685 cab 2067 wnfc 2206 crab 2352 wsbc 2815 csb 2908 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 df-sbc 2816 df-csb 2909 |
This theorem is referenced by: (None) |
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