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Mirrors > Home > ILE Home > Th. List > cbvreucsf | Unicode version |
Description: A more general version of cbvreuv 2633 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 1493 | . . . 4 | |
2 | nfcsb1v 3005 | . . . . . 6 | |
3 | 2 | nfcri 2252 | . . . . 5 |
4 | nfs1v 1892 | . . . . 5 | |
5 | 3, 4 | nfan 1529 | . . . 4 |
6 | id 19 | . . . . . 6 | |
7 | csbeq1a 2983 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2188 | . . . . 5 |
9 | sbequ12 1729 | . . . . 5 | |
10 | 8, 9 | anbi12d 464 | . . . 4 |
11 | 1, 5, 10 | cbveu 2001 | . . 3 |
12 | nfcv 2258 | . . . . . . 7 | |
13 | cbvralcsf.1 | . . . . . . 7 | |
14 | 12, 13 | nfcsb 3007 | . . . . . 6 |
15 | 14 | nfcri 2252 | . . . . 5 |
16 | cbvralcsf.3 | . . . . . 6 | |
17 | 16 | nfsb 1899 | . . . . 5 |
18 | 15, 17 | nfan 1529 | . . . 4 |
19 | nfv 1493 | . . . 4 | |
20 | id 19 | . . . . . 6 | |
21 | csbeq1 2978 | . . . . . . 7 | |
22 | sbsbc 2886 | . . . . . . . . 9 | |
23 | 22 | abbii 2233 | . . . . . . . 8 |
24 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
25 | 24 | nfcri 2252 | . . . . . . . . . . 11 |
26 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
27 | 26 | eleq2d 2187 | . . . . . . . . . . 11 |
28 | 25, 27 | sbie 1749 | . . . . . . . . . 10 |
29 | 28 | bicomi 131 | . . . . . . . . 9 |
30 | 29 | abbi2i 2232 | . . . . . . . 8 |
31 | df-csb 2976 | . . . . . . . 8 | |
32 | 23, 30, 31 | 3eqtr4ri 2149 | . . . . . . 7 |
33 | 21, 32 | syl6eq 2166 | . . . . . 6 |
34 | 20, 33 | eleq12d 2188 | . . . . 5 |
35 | sbequ 1796 | . . . . . 6 | |
36 | cbvralcsf.4 | . . . . . . 7 | |
37 | cbvralcsf.6 | . . . . . . 7 | |
38 | 36, 37 | sbie 1749 | . . . . . 6 |
39 | 35, 38 | syl6bb 195 | . . . . 5 |
40 | 34, 39 | anbi12d 464 | . . . 4 |
41 | 18, 19, 40 | cbveu 2001 | . . 3 |
42 | 11, 41 | bitri 183 | . 2 |
43 | df-reu 2400 | . 2 | |
44 | df-reu 2400 | . 2 | |
45 | 42, 43, 44 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wnf 1421 wcel 1465 wsb 1720 weu 1977 cab 2103 wnfc 2245 wreu 2395 wsbc 2882 csb 2975 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-reu 2400 df-sbc 2883 df-csb 2976 |
This theorem is referenced by: (None) |
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