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Mirrors > Home > ILE Home > Th. List > cbvoprab1 | Unicode version |
Description: Rule used to change first bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 20-Dec-2008.) (Revised by Mario Carneiro, 5-Dec-2016.) |
Ref | Expression |
---|---|
cbvoprab1.1 | |
cbvoprab1.2 | |
cbvoprab1.3 |
Ref | Expression |
---|---|
cbvoprab1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . . . 6 | |
2 | cbvoprab1.1 | . . . . . 6 | |
3 | 1, 2 | nfan 1457 | . . . . 5 |
4 | 3 | nfex 1528 | . . . 4 |
5 | nfv 1421 | . . . . . 6 | |
6 | cbvoprab1.2 | . . . . . 6 | |
7 | 5, 6 | nfan 1457 | . . . . 5 |
8 | 7 | nfex 1528 | . . . 4 |
9 | opeq1 3549 | . . . . . . 7 | |
10 | 9 | eqeq2d 2051 | . . . . . 6 |
11 | cbvoprab1.3 | . . . . . 6 | |
12 | 10, 11 | anbi12d 442 | . . . . 5 |
13 | 12 | exbidv 1706 | . . . 4 |
14 | 4, 8, 13 | cbvex 1639 | . . 3 |
15 | 14 | opabbii 3824 | . 2 |
16 | dfoprab2 5552 | . 2 | |
17 | dfoprab2 5552 | . 2 | |
18 | 15, 16, 17 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wnf 1349 wex 1381 cop 3378 copab 3817 coprab 5513 |
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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-opab 3819 df-oprab 5516 |
This theorem is referenced by: (None) |
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