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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 1544 | . . . . 5 |
4 | 3 | nfex 1616 | . . . 4 |
5 | 4 | nfex 1616 | . . 3 |
6 | nfv 1508 | . . . . . 6 | |
7 | cbvoprab3.2 | . . . . . 6 | |
8 | 6, 7 | nfan 1544 | . . . . 5 |
9 | 8 | nfex 1616 | . . . 4 |
10 | 9 | nfex 1616 | . . 3 |
11 | cbvoprab3.3 | . . . . 5 | |
12 | 11 | anbi2d 459 | . . . 4 |
13 | 12 | 2exbidv 1840 | . . 3 |
14 | 5, 10, 13 | cbvopab2 3997 | . 2 |
15 | dfoprab2 5811 | . 2 | |
16 | dfoprab2 5811 | . 2 | |
17 | 14, 15, 16 | 3eqtr4i 2168 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wnf 1436 wex 1468 cop 3525 copab 3983 coprab 5768 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-opab 3985 df-oprab 5771 |
This theorem is referenced by: cbvoprab3v 5841 tposoprab 6170 erovlem 6514 |
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