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Mirrors > Home > ILE Home > Th. List > cbvrexcsf | Unicode version |
Description: A more general version of cbvrexf 2528 that has no distinct variable restrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) (Proof shortened by Mario Carneiro, 7-Dec-2014.) |
Ref | Expression |
---|---|
cbvralcsf.1 | |
cbvralcsf.2 | |
cbvralcsf.3 | |
cbvralcsf.4 | |
cbvralcsf.5 | |
cbvralcsf.6 |
Ref | Expression |
---|---|
cbvrexcsf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . 4 | |
2 | nfcsb1v 2882 | . . . . . 6 | |
3 | 2 | nfcri 2172 | . . . . 5 |
4 | nfsbc1v 2782 | . . . . 5 | |
5 | 3, 4 | nfan 1457 | . . . 4 |
6 | id 19 | . . . . . 6 | |
7 | csbeq1a 2860 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2108 | . . . . 5 |
9 | sbceq1a 2773 | . . . . 5 | |
10 | 8, 9 | anbi12d 442 | . . . 4 |
11 | 1, 5, 10 | cbvex 1639 | . . 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 | 12, 16 | nfsbc 2784 | . . . . 5 |
18 | 15, 17 | nfan 1457 | . . . 4 |
19 | nfv 1421 | . . . 4 | |
20 | id 19 | . . . . . 6 | |
21 | csbeq1 2855 | . . . . . . 7 | |
22 | df-csb 2853 | . . . . . . . 8 | |
23 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
24 | 23 | nfcri 2172 | . . . . . . . . . . 11 |
25 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
26 | 25 | eleq2d 2107 | . . . . . . . . . . 11 |
27 | 24, 26 | sbie 1674 | . . . . . . . . . 10 |
28 | sbsbc 2768 | . . . . . . . . . 10 | |
29 | 27, 28 | bitr3i 175 | . . . . . . . . 9 |
30 | 29 | abbi2i 2152 | . . . . . . . 8 |
31 | 22, 30 | eqtr4i 2063 | . . . . . . 7 |
32 | 21, 31 | syl6eq 2088 | . . . . . 6 |
33 | 20, 32 | eleq12d 2108 | . . . . 5 |
34 | dfsbcq 2766 | . . . . . 6 | |
35 | sbsbc 2768 | . . . . . . 7 | |
36 | cbvralcsf.4 | . . . . . . . 8 | |
37 | cbvralcsf.6 | . . . . . . . 8 | |
38 | 36, 37 | sbie 1674 | . . . . . . 7 |
39 | 35, 38 | bitr3i 175 | . . . . . 6 |
40 | 34, 39 | syl6bb 185 | . . . . 5 |
41 | 33, 40 | anbi12d 442 | . . . 4 |
42 | 18, 19, 41 | cbvex 1639 | . . 3 |
43 | 11, 42 | bitri 173 | . 2 |
44 | df-rex 2312 | . 2 | |
45 | df-rex 2312 | . 2 | |
46 | 43, 44, 45 | 3bitr4i 201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wex 1381 wcel 1393 wsb 1645 cab 2026 wnfc 2165 wrex 2307 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-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: cbvrexv2 2913 |
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