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Mirrors > Home > NFE 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 1619 | . . . 4 | |
2 | cbvrab.1 | . . . . . 6 | |
3 | 2 | nfcri 2483 | . . . . 5 |
4 | nfs1v 2106 | . . . . 5 | |
5 | 3, 4 | nfan 1824 | . . . 4 |
6 | eleq1 2413 | . . . . 5 | |
7 | sbequ12 1919 | . . . . 5 | |
8 | 6, 7 | anbi12d 691 | . . . 4 |
9 | 1, 5, 8 | cbvab 2471 | . . 3 |
10 | cbvrab.2 | . . . . . 6 | |
11 | 10 | nfcri 2483 | . . . . 5 |
12 | cbvrab.3 | . . . . . 6 | |
13 | 12 | nfsb 2109 | . . . . 5 |
14 | 11, 13 | nfan 1824 | . . . 4 |
15 | nfv 1619 | . . . 4 | |
16 | eleq1 2413 | . . . . 5 | |
17 | sbequ 2060 | . . . . . 6 | |
18 | cbvrab.4 | . . . . . . 7 | |
19 | cbvrab.5 | . . . . . . 7 | |
20 | 18, 19 | sbie 2038 | . . . . . 6 |
21 | 17, 20 | syl6bb 252 | . . . . 5 |
22 | 16, 21 | anbi12d 691 | . . . 4 |
23 | 14, 15, 22 | cbvab 2471 | . . 3 |
24 | 9, 23 | eqtri 2373 | . 2 |
25 | df-rab 2623 | . 2 | |
26 | df-rab 2623 | . 2 | |
27 | 24, 25, 26 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wnf 1544 wceq 1642 wsb 1648 wcel 1710 cab 2339 wnfc 2476 crab 2618 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rab 2623 |
This theorem is referenced by: cbvrabv 2858 elrabsf 3084 |
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