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Mirrors > Home > ILE Home > Th. List > cbvoprab2 | Unicode version |
Description: Change the second bound variable in an operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
cbvoprab2.1 | |
cbvoprab2.2 | |
cbvoprab2.3 |
Ref | Expression |
---|---|
cbvoprab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1521 | . . . . . . 7 | |
2 | cbvoprab2.1 | . . . . . . 7 | |
3 | 1, 2 | nfan 1558 | . . . . . 6 |
4 | 3 | nfex 1630 | . . . . 5 |
5 | nfv 1521 | . . . . . . 7 | |
6 | cbvoprab2.2 | . . . . . . 7 | |
7 | 5, 6 | nfan 1558 | . . . . . 6 |
8 | 7 | nfex 1630 | . . . . 5 |
9 | opeq2 3766 | . . . . . . . . 9 | |
10 | 9 | opeq1d 3771 | . . . . . . . 8 |
11 | 10 | eqeq2d 2182 | . . . . . . 7 |
12 | cbvoprab2.3 | . . . . . . 7 | |
13 | 11, 12 | anbi12d 470 | . . . . . 6 |
14 | 13 | exbidv 1818 | . . . . 5 |
15 | 4, 8, 14 | cbvex 1749 | . . . 4 |
16 | 15 | exbii 1598 | . . 3 |
17 | 16 | abbii 2286 | . 2 |
18 | df-oprab 5857 | . 2 | |
19 | df-oprab 5857 | . 2 | |
20 | 17, 18, 19 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wnf 1453 wex 1485 cab 2156 cop 3586 coprab 5854 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-oprab 5857 |
This theorem is referenced by: (None) |
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