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Mirrors > Home > ILE Home > Th. List > cbvrexcsf | Unicode version |
Description: A more general version of cbvrexf 2649 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 1508 | . . . 4 | |
2 | nfcsb1v 3035 | . . . . . 6 | |
3 | 2 | nfcri 2275 | . . . . 5 |
4 | nfsbc1v 2927 | . . . . 5 | |
5 | 3, 4 | nfan 1544 | . . . 4 |
6 | id 19 | . . . . . 6 | |
7 | csbeq1a 3012 | . . . . . 6 | |
8 | 6, 7 | eleq12d 2210 | . . . . 5 |
9 | sbceq1a 2918 | . . . . 5 | |
10 | 8, 9 | anbi12d 464 | . . . 4 |
11 | 1, 5, 10 | cbvex 1729 | . . 3 |
12 | nfcv 2281 | . . . . . . 7 | |
13 | cbvralcsf.1 | . . . . . . 7 | |
14 | 12, 13 | nfcsb 3037 | . . . . . 6 |
15 | 14 | nfcri 2275 | . . . . 5 |
16 | cbvralcsf.3 | . . . . . 6 | |
17 | 12, 16 | nfsbc 2929 | . . . . 5 |
18 | 15, 17 | nfan 1544 | . . . 4 |
19 | nfv 1508 | . . . 4 | |
20 | id 19 | . . . . . 6 | |
21 | csbeq1 3006 | . . . . . . 7 | |
22 | df-csb 3004 | . . . . . . . 8 | |
23 | cbvralcsf.2 | . . . . . . . . . . . 12 | |
24 | 23 | nfcri 2275 | . . . . . . . . . . 11 |
25 | cbvralcsf.5 | . . . . . . . . . . . 12 | |
26 | 25 | eleq2d 2209 | . . . . . . . . . . 11 |
27 | 24, 26 | sbie 1764 | . . . . . . . . . 10 |
28 | sbsbc 2913 | . . . . . . . . . 10 | |
29 | 27, 28 | bitr3i 185 | . . . . . . . . 9 |
30 | 29 | abbi2i 2254 | . . . . . . . 8 |
31 | 22, 30 | eqtr4i 2163 | . . . . . . 7 |
32 | 21, 31 | syl6eq 2188 | . . . . . 6 |
33 | 20, 32 | eleq12d 2210 | . . . . 5 |
34 | dfsbcq 2911 | . . . . . 6 | |
35 | sbsbc 2913 | . . . . . . 7 | |
36 | cbvralcsf.4 | . . . . . . . 8 | |
37 | cbvralcsf.6 | . . . . . . . 8 | |
38 | 36, 37 | sbie 1764 | . . . . . . 7 |
39 | 35, 38 | bitr3i 185 | . . . . . 6 |
40 | 34, 39 | syl6bb 195 | . . . . 5 |
41 | 33, 40 | anbi12d 464 | . . . 4 |
42 | 18, 19, 41 | cbvex 1729 | . . 3 |
43 | 11, 42 | bitri 183 | . 2 |
44 | df-rex 2422 | . 2 | |
45 | df-rex 2422 | . 2 | |
46 | 43, 44, 45 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wex 1468 wcel 1480 wsb 1735 cab 2125 wnfc 2268 wrex 2417 wsbc 2909 csb 3003 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-sbc 2910 df-csb 3004 |
This theorem is referenced by: cbvrexv2 3067 |
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