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Mirrors > Home > ILE Home > Th. List > cbvoprab3 | Unicode version |
Description: Rule used to change the third bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 22-Aug-2013.) |
Ref | Expression |
---|---|
cbvoprab3.1 | |
cbvoprab3.2 | |
cbvoprab3.3 |
Ref | Expression |
---|---|
cbvoprab3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . . . . . 6 | |
2 | cbvoprab3.1 | . . . . . 6 | |
3 | 1, 2 | nfan 1545 | . . . . 5 |
4 | 3 | nfex 1617 | . . . 4 |
5 | 4 | nfex 1617 | . . 3 |
6 | nfv 1508 | . . . . . 6 | |
7 | cbvoprab3.2 | . . . . . 6 | |
8 | 6, 7 | nfan 1545 | . . . . 5 |
9 | 8 | nfex 1617 | . . . 4 |
10 | 9 | nfex 1617 | . . 3 |
11 | cbvoprab3.3 | . . . . 5 | |
12 | 11 | anbi2d 460 | . . . 4 |
13 | 12 | 2exbidv 1848 | . . 3 |
14 | 5, 10, 13 | cbvopab2 4038 | . 2 |
15 | dfoprab2 5868 | . 2 | |
16 | dfoprab2 5868 | . 2 | |
17 | 14, 15, 16 | 3eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wnf 1440 wex 1472 cop 3563 copab 4024 coprab 5825 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4026 df-oprab 5828 |
This theorem is referenced by: cbvoprab3v 5898 tposoprab 6227 erovlem 6572 |
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