Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > cbvreucsf | Unicode version |
Description: A more general version of cbvreuv 2535 that has no distinct variable rextrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) |
Ref | Expression |
---|---|
cbvralcsf.1 | |
cbvralcsf.2 | |
cbvralcsf.3 | |
cbvralcsf.4 | |
cbvralcsf.5 | |
cbvralcsf.6 |
Ref | Expression |
---|---|
cbvreucsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . 4 | |
2 | nfcsb1v 2882 | . . . . . 6 | |
3 | 2 | nfcri 2172 | . . . . 5 |
4 | nfs1v 1815 | . . . . 5 | |
5 | 3, 4 | nfan 1457 | . . . 4 |
6 | id 19 | . . . . . 6 | |
7 | csbeq1a 2860 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2108 | . . . . 5 |
9 | sbequ12 1654 | . . . . 5 | |
10 | 8, 9 | anbi12d 442 | . . . 4 |
11 | 1, 5, 10 | cbveu 1924 | . . 3 |
12 | nfcv 2178 | . . . . . . 7 | |
13 | cbvralcsf.1 | . . . . . . 7 | |
14 | 12, 13 | nfcsb 2884 | . . . . . 6 |
15 | 14 | nfcri 2172 | . . . . 5 |
16 | cbvralcsf.3 | . . . . . 6 | |
17 | 16 | nfsb 1822 | . . . . 5 |
18 | 15, 17 | nfan 1457 | . . . 4 |
19 | nfv 1421 | . . . 4 | |
20 | id 19 | . . . . . 6 | |
21 | csbeq1 2855 | . . . . . . 7 | |
22 | sbsbc 2768 | . . . . . . . . 9 | |
23 | 22 | abbii 2153 | . . . . . . . 8 |
24 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
25 | 24 | nfcri 2172 | . . . . . . . . . . 11 |
26 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
27 | 26 | eleq2d 2107 | . . . . . . . . . . 11 |
28 | 25, 27 | sbie 1674 | . . . . . . . . . 10 |
29 | 28 | bicomi 123 | . . . . . . . . 9 |
30 | 29 | abbi2i 2152 | . . . . . . . 8 |
31 | df-csb 2853 | . . . . . . . 8 | |
32 | 23, 30, 31 | 3eqtr4ri 2071 | . . . . . . 7 |
33 | 21, 32 | syl6eq 2088 | . . . . . 6 |
34 | 20, 33 | eleq12d 2108 | . . . . 5 |
35 | sbequ 1721 | . . . . . 6 | |
36 | cbvralcsf.4 | . . . . . . 7 | |
37 | cbvralcsf.6 | . . . . . . 7 | |
38 | 36, 37 | sbie 1674 | . . . . . 6 |
39 | 35, 38 | syl6bb 185 | . . . . 5 |
40 | 34, 39 | anbi12d 442 | . . . 4 |
41 | 18, 19, 40 | cbveu 1924 | . . 3 |
42 | 11, 41 | bitri 173 | . 2 |
43 | df-reu 2313 | . 2 | |
44 | df-reu 2313 | . 2 | |
45 | 42, 43, 44 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wcel 1393 wsb 1645 weu 1900 cab 2026 wnfc 2165 wreu 2308 wsbc 2764 csb 2852 |
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-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-reu 2313 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |