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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 1515 | . . . . . . 7 | |
2 | cbvoprab2.1 | . . . . . . 7 | |
3 | 1, 2 | nfan 1552 | . . . . . 6 |
4 | 3 | nfex 1624 | . . . . 5 |
5 | nfv 1515 | . . . . . . 7 | |
6 | cbvoprab2.2 | . . . . . . 7 | |
7 | 5, 6 | nfan 1552 | . . . . . 6 |
8 | 7 | nfex 1624 | . . . . 5 |
9 | opeq2 3753 | . . . . . . . . 9 | |
10 | 9 | opeq1d 3758 | . . . . . . . 8 |
11 | 10 | eqeq2d 2176 | . . . . . . 7 |
12 | cbvoprab2.3 | . . . . . . 7 | |
13 | 11, 12 | anbi12d 465 | . . . . . 6 |
14 | 13 | exbidv 1812 | . . . . 5 |
15 | 4, 8, 14 | cbvex 1743 | . . . 4 |
16 | 15 | exbii 1592 | . . 3 |
17 | 16 | abbii 2280 | . 2 |
18 | df-oprab 5840 | . 2 | |
19 | df-oprab 5840 | . 2 | |
20 | 17, 18, 19 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wnf 1447 wex 1479 cab 2150 cop 3573 coprab 5837 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-oprab 5840 |
This theorem is referenced by: (None) |
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