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Mirrors > Home > ILE Home > Th. List > cbvrab | Unicode version |
Description: Rule to change the bound variable in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 9-Oct-2016.) |
Ref | Expression |
---|---|
cbvrab.1 | |
cbvrab.2 | |
cbvrab.3 | |
cbvrab.4 | |
cbvrab.5 |
Ref | Expression |
---|---|
cbvrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1461 | . . . 4 | |
2 | cbvrab.1 | . . . . . 6 | |
3 | 2 | nfcri 2213 | . . . . 5 |
4 | nfs1v 1856 | . . . . 5 | |
5 | 3, 4 | nfan 1497 | . . . 4 |
6 | eleq1 2141 | . . . . 5 | |
7 | sbequ12 1694 | . . . . 5 | |
8 | 6, 7 | anbi12d 456 | . . . 4 |
9 | 1, 5, 8 | cbvab 2201 | . . 3 |
10 | cbvrab.2 | . . . . . 6 | |
11 | 10 | nfcri 2213 | . . . . 5 |
12 | cbvrab.3 | . . . . . 6 | |
13 | 12 | nfsb 1863 | . . . . 5 |
14 | 11, 13 | nfan 1497 | . . . 4 |
15 | nfv 1461 | . . . 4 | |
16 | eleq1 2141 | . . . . 5 | |
17 | sbequ 1761 | . . . . . 6 | |
18 | cbvrab.4 | . . . . . . 7 | |
19 | cbvrab.5 | . . . . . . 7 | |
20 | 18, 19 | sbie 1714 | . . . . . 6 |
21 | 17, 20 | syl6bb 194 | . . . . 5 |
22 | 16, 21 | anbi12d 456 | . . . 4 |
23 | 14, 15, 22 | cbvab 2201 | . . 3 |
24 | 9, 23 | eqtri 2101 | . 2 |
25 | df-rab 2357 | . 2 | |
26 | df-rab 2357 | . 2 | |
27 | 24, 25, 26 | 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 |
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-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rab 2357 |
This theorem is referenced by: cbvrabv 2600 elrabsf 2852 tfis 4324 |
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